Relevant bibliographies by topics / Measure Theoretic Probability Theory

Contents

  1. Journal articles
  2. Dissertations / Theses
  3. Books
  4. Book chapters
  5. Conference papers

Academic literature on the topic 'Measure Theoretic Probability Theory'

Author: Grafiati
Published: 4 June 2021
Last updated: 8 February 2022

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Journal articles on the topic "Measure Theoretic Probability Theory"

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KUYPER, RUTGER, and SEBASTIAAN A. TERWIJN. "MODEL THEORY OF MEASURE SPACES AND PROBABILITY LOGIC." Review of Symbolic Logic 6, no. 3 (April 8, 2013): 367–93. http://dx.doi.org/10.1017/s1755020313000063.

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AbstractWe study the model-theoretic aspects of a probability logic suited for talking about measure spaces. This nonclassical logic has a model theory rather different from that of classical predicate logic. In general, not every satisfiable set of sentences has a countable model, but we show that one can always build a model on the unit interval. Also, the probability logic under consideration is not compact. However, using ultraproducts we can prove a compactness theorem for a certain class of weak models.
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Khrennikov, Andrei, Shinichi Yamada, and Arnoud van Rooij. "The measure-theoretical approach to p-adic probability theory." Annales mathématiques Blaise Pascal 6, no. 1 (1999): 21–32. http://dx.doi.org/10.5802/ambp.112.

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Siegmund-Schultze, Reinhard. "Mathematicians Forced to Philosophize: An Introduction to Khinchin's Paper on von Mises' Theory of Probability." Science in Context 17, no. 3 (September 2004): 373–90. http://dx.doi.org/10.1017/s0269889704000171.

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What follows shall provide an introduction to a predominantly philosophical and polemical, but historically revealing, paper on the foundations of the theory of probability. The leading Russian probabilist Aleksandr Yakovlevich Khinchin (1894–1959) (see fig. 1) wrote the paper in the late 1930s, commenting on a slightly older, but still competing approach to probability theory by Richard von Mises. Together with the even more influential Andrey Nikolayevich Kolmogorov (1903–1987), who was nine years his junior, Khinchin had revolutionized probability theory around 1930 by introducing the modern measure-theoretic approach, which is still standard today and which allowed for a sufficiently general treatment of important new notions such as “stochastic processes.” This development had its first culmination in Kolmogorov's booklet, Grundbegriffe der Wahrscheinlichkeitsrechnung, written in German in 1933, which has exerted an enormous influence world wide.
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Pei, Han Ru, Zhi Jian Wang, and Yu Wang. "Bayesian Inference of Information Theoretic Metrics of Anonymity." Advanced Materials Research 989-994 (July 2014): 4680–83. http://dx.doi.org/10.4028/www.scientific.net/amr.989-994.4680.

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Information theoretic metrics is popular theory to measure anonymity. However the difficulty in getting the probability distribution of subjects hampers its practical usage. In this paper we propose a Bayesian inference method to tackle this problem. Our method makes it possible to compare the anonymity of different anonymous systems. We use this method to analyze Threshold Mix and point out different system parameters which do and do not have influence on anonymity.
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Bingham, N. H. "Doob: A Half-Century on." Journal of Applied Probability 42, no. 01 (March 2005): 257–66. http://dx.doi.org/10.1017/s0021900200000206.

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Probability theory, and its dynamic aspect stochastic process theory, is both a venerable subject, in that its roots go back to the mid-seventeenth century, and a young one, in that its modern formulation happened comparatively recently - well within living memory. The year 2003 marked the seventieth anniversary of Kolmogorov's Grundbegriffe der Wahrscheinlichkeitsrechnung, usually regarded as having inaugurated modern (measure-theoretic) probability theory. It also marked the fiftieth anniversary of Doob's Stochastic Processes. The profound and continuing influence of this classic work prompts the present piece.
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Bingham, N. H. "Doob: A Half-Century on." Journal of Applied Probability 42, no. 1 (March 2005): 257–66. http://dx.doi.org/10.1239/jap/1110381385.

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Probability theory, and its dynamic aspect stochastic process theory, is both a venerable subject, in that its roots go back to the mid-seventeenth century, and a young one, in that its modern formulation happened comparatively recently - well within living memory. The year 2003 marked the seventieth anniversary of Kolmogorov'sGrundbegriffe der Wahrscheinlichkeitsrechnung, usually regarded as having inaugurated modern (measure-theoretic) probability theory. It also marked the fiftieth anniversary of Doob'sStochastic Processes. The profound and continuing influence of this classic work prompts the present piece.
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Cho, Kenta, and Bart Jacobs. "Disintegration and Bayesian inversion via string diagrams." Mathematical Structures in Computer Science 29, no. 7 (March 13, 2019): 938–71. http://dx.doi.org/10.1017/s0960129518000488.

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AbstractThe notions of disintegration and Bayesian inversion are fundamental in conditional probability theory. They produce channels, as conditional probabilities, from a joint state, or from an already given channel (in opposite direction). These notions exist in the literature, in concrete situations, but are presented here in abstract graphical formulations. The resulting abstract descriptions are used for proving basic results in conditional probability theory. The existence of disintegration and Bayesian inversion is discussed for discrete probability, and also for measure-theoretic probability – via standard Borel spaces and via likelihoods. Finally, the usefulness of disintegration and Bayesian inversion is illustrated in several examples.
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Fritz, Tobias, and Eigil Fjeldgren Rischel. "Infinite products and zero-one laws in categorical probability." Compositionality 2 (August 11, 2020): 3. http://dx.doi.org/10.32408/compositionality-2-3.

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Markov categories are a recent category-theoretic approach to the foundations of probability and statistics. Here we develop this approach further by treating infinite products and the Kolmogorov extension theorem. This is relevant for all aspects of probability theory in which infinitely many random variables appear at a time. These infinite tensor products ⨂i∈JXi come in two versions: a weaker but more general one for families of objects (Xi)i∈J in semicartesian symmetric monoidal categories, and a stronger but more specific one for families of objects in Markov categories.As a first application, we state and prove versions of the zero--one laws of Kolmogorov and Hewitt--Savage for Markov categories. This gives general versions of these results which can be instantiated not only in measure-theoretic probability, where they specialize to the standard ones in the setting of standard Borel spaces, but also in other contexts.
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Nowak, Piotr, and Olgierd Hryniewicz. "On MV-Algebraic Versions of the Strong Law of Large Numbers." Entropy 21, no. 7 (July 19, 2019): 710. http://dx.doi.org/10.3390/e21070710.

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Many-valued (MV; the many-valued logics considered by Łukasiewicz)-algebras are algebraic systems that generalize Boolean algebras. The MV-algebraic probability theory involves the notions of the state and observable, which abstract the probability measure and the random variable, both considered in the Kolmogorov probability theory. Within the MV-algebraic probability theory, many important theorems (such as various versions of the central limit theorem or the individual ergodic theorem) have been recently studied and proven. In particular, the counterpart of the Kolmogorov strong law of large numbers (SLLN) for sequences of independent observables has been considered. In this paper, we prove generalized MV-algebraic versions of the SLLN, i.e., counterparts of the Marcinkiewicz–Zygmund and Brunk–Prokhorov SLLN for independent observables, as well as the Korchevsky SLLN, where the independence of observables is not assumed. To this end, we apply the classical probability theory and some measure-theoretic methods. We also analyze examples of applications of the proven theorems. Our results open new directions of development of the MV-algebraic probability theory. They can also be applied to the problem of entropy estimation.
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Tonn, B. E., and A. Schaffhauser. "Towards a More General Theoretical and Mathematical Model of Probability for Policy Analysis." Environment and Planning A: Economy and Space 24, no. 9 (September 1992): 1337–53. http://dx.doi.org/10.1068/a241337.

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Uncertainty pervades policy analysis in ways that transcend classical concepts of probability. To benefit policy analysis, the concept of probability must be considerably broadened. It is argued that probability can be conceptualized with respect to the characteristics of policy problems that produce inherent uncertainty. Problems that encompass uncertainty can be characterized according to their: (1) fundamental requirements, for example forecasting, knowledge creation, fact establishment; (2) system properties such as disorderly versus orderly systems; (3) problem-solution strategy, for example subjective judgement, model-based analysis, data analysis; (4) problem-solution data requirements—from numerous and hard-to-measure variables to few and easy-to-measure variables, and (5) problem-solution frame—ranging from unbounded solution spaces to small and discrete solution spaces. The theory of lower probability is presented as a generalization of classical additive probability that can handle this generalized conceptualization of probability. Information-theoretic methods for integrating the two generalizations of probability are considered.
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Dissertations / Theses on the topic "Measure Theoretic Probability Theory"

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Knowles, Bryan A. "In the Face of Anticipation: Decision Making under Visible Uncertainty as Present in the Safest-with-Sight Problem." TopSCHOLAR®, 2016. http://digitalcommons.wku.edu/theses/1565.

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Pathfinding, as a process of selecting a fixed route, has long been studied in Computer Science and Mathematics. Decision making, as a similar, but intrinsically different, process of determining a control policy, is much less studied. Here, I propose a problem that appears to be of the first class, which would suggest that it is easily solvable with a modern machine, but that would be too easy, it turns out. By allowing a pathfinding to anticipate and respond to information, without setting restrictions on the \structure" of this anticipation, selecting the \best step" appears to be an intractable problem. After introducing the necessary foundations and stepping through the strangeness of “safest-with-sight," I attempt to develop an method of approximating the success rate associated with each potential decision; the results suggest something fundamental about decision making itself, that information that is collected at a moment that it is not immediately “consumable", i.e. non-incident, is not as necessary to anticipate than the contrary, i.e. incident information. This is significant because (i) it speaks about when the information should be anticipated, a moment in decision-making long before the information is actually collected, and (ii) whenever the model is restricted to only incident anticipation the problem again becomes tractable. When we only anticipate what is most important, solutions become easy to compute, but attempting to anticipate any more than that and solutions may become impossible to find on any realistic machine.
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Etheridge, Alison Mary. "Asymptotic behaviour of some measure-valued diffusions." Thesis, University of Oxford, 1989. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.329943.

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Youmbi, Norbert. "Probability theory on semihypergroups." [Tampa, Fla.] : University of South Florida, 2005. http://purl.fcla.edu/fcla/etd/SFE0001201.

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Yu, Hua. "Neutral zone classifiers within a decision-theoretic framework." Diss., UC access only, 2009. http://gateway.proquest.com/openurl?url_ver=Z39.88-2004&rft_val_fmt=info:ofi/fmt:kev:mtx:dissertation&res_dat=xri:pqdiss&rft_dat=xri:pqdiss:3357008.

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Thesis (Ph. D.)--University of California, Riverside, 2009.
Includes abstract. Also issued in print. Includes bibliographical references (leaves 81-84). Available via ProQuest Digital Dissertations.
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Bass, Jeremiah Joseph. "Mycielski-Regular Measures." Thesis, University of North Texas, 2011. https://digital.library.unt.edu/ark:/67531/metadc84171/.

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Let μ be a Radon probability measure on M, the d-dimensional Real Euclidean space (where d is a positive integer), and f a measurable function. Let P be the space of sequences whose coordinates are elements in M. Then, for any point x in M, define a function ƒn on M and P that looks at the first n terms of an element of P and evaluates f at the first of those n terms that minimizes the distance to x in M. The measures for which such sequences converge in measure to f for almost every sequence are called Mycielski-regular. We show that the self-similar measure generated by a finite family of contracting similitudes and which up to a constant is the Hausdorff measure in its dimension on an invariant set C is Mycielski-regular.
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Liang, Jing Yi. "Response data compaction in BIST under generalized mergeability based on switching theory formulation and utilizing a new measure of failure probability." Thesis, National Library of Canada = Bibliothèque nationale du Canada, 2000. http://www.collectionscanada.ca/obj/s4/f2/dsk1/tape4/PQDD_0018/MQ58478.pdf.

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Toronto, Neil B. "Trustworthy, Useful Languages for Probabilistic Modeling and Inference." BYU ScholarsArchive, 2014. https://scholarsarchive.byu.edu/etd/4098.

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The ideals of exact modeling, and of putting off approximations as long as possible, make Bayesian practice both successful and difficult. Languages for modeling probabilistic processes, whose implementations answer questions about them under asserted conditions, promise to ease much of the difficulty. Unfortunately, very few of these languages have mathematical specifications. This makes them difficult to trust: there is no way to distinguish between an implementation error and a feature, and there is no standard by which to prove optimizations correct. Further, because the languages are based on the incomplete theories of probability typically used in Bayesian practice, they place seemingly artificial restrictions on legal programs and questions, such as disallowing unbounded recursion and allowing only simple equality conditions. We prove it is possible to make trustworthy probabilistic languages for Bayesian practice by using functional programming theory to define them mathematically and prove them correct. The specifications interpret programs using measure-theoretic probability, which is a complete enough theory of probability that we do not need to restrict programs or conditions. We demonstrate that these trustworthy languages are useful by implementing them, and using them to model and answer questions about typical probabilistic processes. We also model and answer questions about processes that are either difficult or impossible to reason about precisely using typical Bayesian mathematical tools.
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Rowley, Jordan M. "The Martingale Approach to Financial Mathematics." DigitalCommons@CalPoly, 2019. https://digitalcommons.calpoly.edu/theses/2014.

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In this thesis, we will develop the fundamental properties of financial mathematics, with a focus on establishing meaningful connections between martingale theory, stochastic calculus, and measure-theoretic probability. We first consider a simple binomial model in discrete time, and assume the impossibility of earning a riskless profit, known as arbitrage. Under this no-arbitrage assumption alone, we stumble upon a strange new probability measure Q, according to which every risky asset is expected to grow as though it were a bond. As it turns out, this measure Q also gives the arbitrage-free pricing formula for every asset on our market. In considering a slightly more complicated model over a finite probability space, we see that Q once again makes its appearance. Finally, in the context of continuous time, we build a framework of stochastic calculus to model the trajectories of asset prices on a finite time interval. Under the absence of arbitrage once more, we see that Q makes its return as a Radon-Nikodym derivative of our initial probability measure. Finally, we use the properties of Q and a stochastic differential equation that models the dynamics of the assets of our market, known as the Ito formula, in order to derive the classic Black-Scholes Equation.
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Damour, Gabriel. "Information-Theoretic Framework for Network Anomaly Detection: Enabling online application of statistical learning models to high-speed traffic." Thesis, KTH, Matematisk statistik, 2019. http://urn.kb.se/resolve?urn=urn:nbn:se:kth:diva-252560.

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With the current proliferation of cyber attacks, safeguarding internet facing assets from network intrusions, is becoming a vital task in our increasingly digitalised economies. Although recent successes of machine learning (ML) models bode the dawn of a new generation of intrusion detection systems (IDS); current solutions struggle to implement these in an efficient manner, leaving many IDSs to rely on rule-based techniques. In this paper we begin by reviewing the different approaches to feature construction and attack source identification employed in such applications. We refer to these steps as the framework within which models are implemented, and use it as a prism through which we can identify the challenges different solutions face, when applied in modern network traffic conditions. Specifically, we discuss how the most popular framework -- the so called flow-based approach -- suffers from significant overhead being introduced by its resource heavy pre-processing step. To address these issues, we propose the Information Theoretic Framework for Network Anomaly Detection (ITF-NAD); whose purpose is to facilitate online application of statistical learning models onto high-speed network links, as well as provide a method of identifying the sources of traffic anomalies. Its development was inspired by previous work on information theoretic-based anomaly and outlier detection, and employs modern techniques of entropy estimation over data streams. Furthermore, a case study of the framework's detection performance over 5 different types of Denial of Service (DoS) attacks is undertaken, in order to illustrate its potential use for intrusion detection and mitigation. The case study resulted in state-of-the-art performance for time-anomaly detection of single source as well as distributed attacks, and show promising results regarding its ability to identify underlying sources.
I takt med att antalet cyberattacker växer snabbt blir det alltmer viktigt för våra digitaliserade ekonomier att skydda uppkopplade verksamheter från nätverksintrång. Maskininlärning (ML) porträtteras som ett kraftfullt alternativ till konventionella regelbaserade lösningar och dess anmärkningsvärda framgångar bådar för en ny generation detekteringssytem mot intrång (IDS). Trots denna utveckling, bygger många IDS:er fortfarande på signaturbaserade metoder, vilket förklaras av de stora svagheter som präglar många ML-baserade lösningar. I detta arbete utgår vi från en granskning av nuvarande forskning kring tillämpningen av ML för intrångsdetektering, med fokus på de nödvändiga steg som omger modellernas implementation inom IDS. Genom att sätta upp ett ramverk för hur variabler konstrueras och identifiering av attackkällor (ASI) utförs i olika lösningar, kan vi identifiera de flaskhalsar och begränsningar som förhindrar deras praktiska implementation. Särskild vikt läggs vid analysen av de populära flödesbaserade modellerna, vars resurskrävande bearbetning av rådata leder till signifikant tidsfördröjning, vilket omöjliggör deras användning i realtidssystem. För att bemöta dessa svagheter föreslår vi ett nytt ramverk -- det informationsteoretiska ramverket för detektering av nätverksanomalier (ITF-NAD) -- vars syfte är att möjliggöra direktanslutning av ML-modeller över nätverkslänkar med höghastighetstrafik, samt tillhandahåller en metod för identifiering av de bakomliggande källorna till attacken. Ramverket bygger på modern entropiestimeringsteknik, designad för att tillämpas över dataströmmar, samt en ASI-metod inspirerad av entropibaserad detektering av avvikande punkter i kategoriska rum. Utöver detta presenteras en studie av ramverkets prestanda över verklig internettrafik, vilken innehåller 5 olika typer av överbelastningsattacker (DoS) genererad från populära DDoS-verktyg, vilket i sin tur illustrerar ramverkets användning med en enkel semi-övervakad ML-modell. Resultaten visar på hög nivå av noggrannhet för detektion av samtliga attacktyper samt lovande prestanda gällande ramverkets förmåga att identifiera de bakomliggande aktörerna.
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Jin, Lei. "Particle systems and SPDEs with application to credit modelling." Thesis, University of Oxford, 2010. http://ora.ox.ac.uk/objects/uuid:07b29609-6941-4aa9-b4bc-29e7b4821b82.

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Books on the topic "Measure Theoretic Probability Theory"

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An introduction to measure-theoretic probability. Boston: Elsevier Academic Press, 2005.

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David, Pollard. A user's guide to measure theoretic probability. Cambridge: Cambridge University Press, 2002.

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Asmussen, Søren. Measure-theoretic foundations of probability theory in Polish spaces. 2nd ed. Copenhagen, Denmark: Institute of Mathematical Statistics, University of Copenhagen, 1987.

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Gallant, A. Ronald. An introduction to econometric theory: Measure-theoretic probability and statistics with applications to economics. Princeton, N.J: Princeton University Press, 1997.

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Fremlin, David Heaver. Set-theoretic measure theory. Colchester: Torres Fremlin, 2008.

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Fremlin, D. H. Set-theoretic measure theory. Colchester: Torres Fremlin, 2008.

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Adams, Malcolm Ritchie. Measure theory and probability. Monterey, Calif: Wadsworth & Brooks/Cole Advanced Books and Software, 1986.

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1937-, Guillemin V., ed. Measure Theory and Probability. Boston, USA: Birkhäuser, 1996.

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Ash, Robert B. Probability and measure theory. 2nd ed. San Diego: Harcourt/Academic Press, 2000.

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Adams, Malcolm, and Victor Guillemin. Measure Theory and Probability. Boston, MA: Birkhäuser Boston, 1996. http://dx.doi.org/10.1007/978-1-4612-0779-5.

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Book chapters on the topic "Measure Theoretic Probability Theory"

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Cohn, Donald L. "Probability." In Measure Theory, 307–71. New York, NY: Springer New York, 2013. http://dx.doi.org/10.1007/978-1-4614-6956-8_10.

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Klenke, Achim. "Basic Measure Theory." In Probability Theory, 1–45. London: Springer London, 2014. http://dx.doi.org/10.1007/978-1-4471-5361-0_1.

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Klenke, Achim. "Basic Measure Theory." In Probability Theory, 1–51. Cham: Springer International Publishing, 2020. http://dx.doi.org/10.1007/978-3-030-56402-5_1.

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Adams, Malcolm, and Victor Guillemin. "Measure Theory." In Measure Theory and Probability, 1–52. Boston, MA: Birkhäuser Boston, 1996. http://dx.doi.org/10.1007/978-1-4612-0779-5_1.

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Hoffmann-Jørgensen, J. "Measure Theory." In Probability with a View Toward Statistics, 1–99. Boston, MA: Springer US, 1994. http://dx.doi.org/10.1007/978-1-4899-3019-4_1.

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Merkle, Milan. "Measure Theory in Probability." In International Encyclopedia of Statistical Science, 793–95. Berlin, Heidelberg: Springer Berlin Heidelberg, 2011. http://dx.doi.org/10.1007/978-3-642-04898-2_360.

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Sullivan, T. J. "Measure and Probability Theory." In Texts in Applied Mathematics, 9–34. Cham: Springer International Publishing, 2015. http://dx.doi.org/10.1007/978-3-319-23395-6_2.

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Kallenberg, Olav. "Measure Theory — Basic Notions." In Probability and Its Applications, 1–22. New York, NY: Springer New York, 2002. http://dx.doi.org/10.1007/978-1-4757-4015-8_1.

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Kallenberg, Olav. "Measure Theory — Key Results." In Probability and Its Applications, 23–44. New York, NY: Springer New York, 2002. http://dx.doi.org/10.1007/978-1-4757-4015-8_2.

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Eisner, Tanja, Bálint Farkas, Markus Haase, and Rainer Nagel. "Measure-Preserving Systems." In Operator Theoretic Aspects of Ergodic Theory, 71–94. Cham: Springer International Publishing, 2015. http://dx.doi.org/10.1007/978-3-319-16898-2_5.

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Conference papers on the topic "Measure Theoretic Probability Theory"

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Cicalese, Ferdinando, Luisa Gargano, and Ugo Vaccaro. "Approximating probability distributions with short vectors, via information theoretic distance measures." In 2016 IEEE International Symposium on Information Theory (ISIT). IEEE, 2016. http://dx.doi.org/10.1109/isit.2016.7541477.

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Cherneva, Zhivelina, C. Guedes Soares, and Petya Petrova. "Distribution of Wave Height Maxima in Storm Sea States." In ASME 2008 27th International Conference on Offshore Mechanics and Arctic Engineering. ASMEDC, 2008. http://dx.doi.org/10.1115/omae2008-58038.

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The effect of the coefficient of kurtosis as a measure of the nonlinearity of third order on the distribution of the wave height maxima has been investigated. Measurements of the surface elevation during a storm at the North Alwyn platform in the North Sea have been used. The mean number of waves in the series is around 100. The maximum wave statistics have been compared with nonlinear theoretical distributions. It was found that the empirical probability densities of the maximum wave heights describe qualitatively the shift of the distribution mode towards higher values. The tendency for the peak of distribution to diminish with increase of the coefficient of kurtosis up to 0.6 is also clearly seen. However, the empirical peak remains higher than the theoretically predicted one. Exceedance probability of the maximum wave heights was also estimated from the data and was compared with the theory. For the highest coefficients of kurtosis nearly 0.6 the theoretical distribution approximates very well the empirical data. For lower coefficients of kurtosis the theory tends to overestimate the exceedance probability of the maximum wave heights.
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Cicalese, Ferdinando, Luisa Gargano, and Ugo Vaccaro. "An Information Theoretic Approach to Probability Mass Function Truncation." In 2019 IEEE International Symposium on Information Theory (ISIT). IEEE, 2019. http://dx.doi.org/10.1109/isit.2019.8849355.

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Atar, Rami, and Neri Merhav. "Information-theoretic applications of the logarithmic probability comparison bound." In 2015 IEEE International Symposium on Information Theory (ISIT). IEEE, 2015. http://dx.doi.org/10.1109/isit.2015.7282552.

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Anderson, Neal G. "An information-theoretic measure for the computational fidelity of physical processes." In 2008 IEEE International Symposium on Information Theory - ISIT. IEEE, 2008. http://dx.doi.org/10.1109/isit.2008.4595412.

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Wierman, Mark J. "Cloud sets as a measure theoretic basis for fuzzy set theory." In NAFIPS 2010 - 2010 Annual Meeting of the North American Fuzzy Information Processing Society. IEEE, 2010. http://dx.doi.org/10.1109/nafips.2010.5548268.

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Chan, T. H., S. Hranilovic, and F. R. Kschischang. "Capacity achieving probability measure of an input-bounded vector gaussian channel." In IEEE International Symposium on Information Theory, 2003. Proceedings. IEEE, 2003. http://dx.doi.org/10.1109/isit.2003.1228387.

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Sason, I., and R. Urbanke. "Information-theoretic lower bounds on the bit error probability of codes on graphs." In IEEE International Symposium on Information Theory, 2003. Proceedings. IEEE, 2003. http://dx.doi.org/10.1109/isit.2003.1228283.

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Witherell, Paul, Sundar Krishnamurty, Ian Grosse, and Jack Wileden. "A meronomic relatedness measure for domain ontologies using concept probability and multiset theory." In NAFIPS 2009 - 2009 Annual Meeting of the North American Fuzzy Information Processing Society. IEEE, 2009. http://dx.doi.org/10.1109/nafips.2009.5156444.

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Ikuta, Akira, and Hisako Orimoto. "Fuzzy Signal Processing of Sound and Electromagnetic Environment by Introducing Probability Measure of Fuzzy Events." In International Conference on Fuzzy Computation Theory and Applications. SCITEPRESS - Science and and Technology Publications, 2014. http://dx.doi.org/10.5220/0005030600050013.

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