Relevant bibliographies by topics / Measurable Projection Theorem

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  2. Dissertations / Theses
  3. Books
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Academic literature on the topic 'Measurable Projection Theorem'

Author: Grafiati
Published: 6 September 2023

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Journal articles on the topic "Measurable Projection Theorem"

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Mateljević, M., and M. Pavlović. "An extension of the Forelli–Rudin projection theorem." Proceedings of the Edinburgh Mathematical Society 36, no. 3 (1993): 375–89. http://dx.doi.org/10.1017/s0013091500018484.

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For a measurable function f on the unit ball B in ℂn we define (M1f)(w), |w|<1, to be the mean modulus of f over a hyperbolic ball with center at w and of a fixed radius. The space , 0<p<∞, is defined by the requirement that M1f belongs to the Lebesgue space Lp. It is shown that the subspace of Lp spanned by holomorphic functions coincides with the corresponding subspace of . It is proved that if s>(n+1)(p−1−1), 0<p<1, then this subspace is complemented in by the projection whose reproducing kernel is . As corollaries we get an extension of the Forelli–Rudin projection theore
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ANTONIOU, IOANNIS, COSTAS KARANIKAS, and STANISLAV SHKARIN. "DECOMPOSITIONS OF SPACES OF MEASURES." Infinite Dimensional Analysis, Quantum Probability and Related Topics 11, no. 01 (2008): 119–26. http://dx.doi.org/10.1142/s0219025708003014.

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Let 𝔐 be the Banach space of σ-additive complex-valued measures on an abstract measurable space. We prove that any closed, with respect to absolute continuity norm-closed, linear subspace L of 𝔐 is complemented and describe the unique complement, projection onto L along which has norm 1. Using this fact we prove a decomposition theorem, which includes the Jordan decomposition theorem, the generalized Radon–Nikodým theorem and the decomposition of measures into decaying and non-decaying components as particular cases. We also prove an analog of the Jessen–Wintner purity theorem for our decompos
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Rzezuchowski, Tadeusz. "Strong convergence of selections implied by weak." Bulletin of the Australian Mathematical Society 39, no. 2 (1989): 201–14. http://dx.doi.org/10.1017/s0004972700002677.

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In some situations weak convergence in L1, implies strong convergence. Let P, L: T → C∘(ℝd) be measurable multifunctions (C∘(ℝd) being the set of closed, convex subsets of ℝd) the values L(t) affine sets and W(t) = P(t) ∩ L(t) extremal faces of P(t). Let pk be integrable selections of P, the projection of pk,(t) on L(t) and pk(t) on W(t). We prove that if converges weakly to zero then pk − k converges to zero in measure. We give also some extensions of this theorem. As applications to differential inclusions we investigate convergence of derivatives of convergent sequences of solutions and we
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Hjorth, Greg. "Bi-Borel reducibility of essentially countable Borel equivalence relations." Journal of Symbolic Logic 70, no. 3 (2005): 979–92. http://dx.doi.org/10.2178/jsl/1122038924.

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This note answers a questions from [2] by showing that considered up to Borel reducibility, there are more essentially countable Borel equivalence relations than countable Borel equivalence relations. Namely:Theorem 0.1. There is an essentially countable Borel equivalence relation E such that for no countable Borel equivalence relation F (on a standard Borel space) do we haveThe proof of the result is short. It does however require an extensive rear guard campaign to extract from the techniques of [1] the followingMessy Fact 0.2. There are countable Borel equivalence relationssuch that:(i) eac
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Gröchenig, Karlheinz, and Philippe Jaming. "THE CRAMÉR–WOLD THEOREM ON QUADRATIC SURFACES AND HEISENBERG UNIQUENESS PAIRS." Journal of the Institute of Mathematics of Jussieu 19, no. 1 (2017): 117–35. http://dx.doi.org/10.1017/s1474748017000457.

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Two measurable sets $S,\unicode[STIX]{x1D6EC}\subseteq \mathbb{R}^{d}$ form a Heisenberg uniqueness pair, if every bounded measure $\unicode[STIX]{x1D707}$ with support in $S$ whose Fourier transform vanishes on $\unicode[STIX]{x1D6EC}$ must be zero. We show that a quadratic hypersurface and the union of two hyperplanes in general position form a Heisenberg uniqueness pair in $\mathbb{R}^{d}$. As a corollary we obtain a new, surprising version of the classical Cramér–Wold theorem: a bounded measure supported on a quadratic hypersurface is uniquely determined by its projections onto two generic
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Hjorth, Greg. "Two Applications of Inner Model Theory to the Study of Sets." Bulletin of Symbolic Logic 2, no. 1 (1996): 94–107. http://dx.doi.org/10.2307/421049.

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§0. Preface. There has been an expectation that the endgame of the more tenacious problems raised by the Los Angeles ‘cabal’ school of descriptive set theory in the 1970's should ultimately be played out with the use of inner model theory. Questions phrased in the language of descriptive set theory, where both the conclusions and the assumptions are couched in terms that only mention simply definable sets of reals, and which have proved resistant to purely descriptive set theoretic arguments, may at last find their solution through the connection between determinacy and large cardinals.Perhaps
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Román-García, Fernando. "Intersections of Projections and Slicing Theorems for the Isotropic Grassmannian and the Heisenberg group." Analysis and Geometry in Metric Spaces 8, no. 1 (2020): 15–35. http://dx.doi.org/10.1515/agms-2020-0002.

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AbstractThis paper studies the Hausdorff dimension of the intersection of isotropic projections of subsets of ℝ2n, as well as dimension of intersections of sets with isotropic planes. It is shown that if A and B are Borel subsets of ℝ2n of dimension greater than m, then for a positive measure set of isotropic m-planes, the intersection of the images of A and B under orthogonal projections onto these planes have positive Hausdorff m-measure. In addition, if A is a measurable set of Hausdorff dimension greater than m, then there is a set B ⊂ ℝ2n with dim B ⩽ m such that for all x ∈ ℝ2n\B there i
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SHI, XIANGHUI. "AXIOM I0 AND HIGHER DEGREE THEORY." Journal of Symbolic Logic 80, no. 3 (2015): 970–1021. http://dx.doi.org/10.1017/jsl.2015.15.

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AbstractIn this paper, we analyze structures of Zermelo degrees via a list of four degree theoretic questions (see §2) in various fine structure extender models, or under large cardinal assumptions. In particular we give a detailed analysis of the structures of Zermelo degrees in the Mitchell model for ω many measurable cardinals. It turns out that there is a profound correlation between the complexity of the degree structures at countable cofinality singular cardinals and the large cardinal strength of the relevant cardinals. The analysis applies to general degree notions, Zermelo degree is m
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Lee, Jaeha, and Izumi Tsutsui. "Quasi-probabilities in conditioned quantum measurement and a geometric/statistical interpretation of Aharonov’s weak value." Progress of Theoretical and Experimental Physics 2017, no. 5 (2017). http://dx.doi.org/10.1093/ptep/ptx024.

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We show that the joint behavior of an arbitrary pair of (generally noncommuting) quantum observables can be described by quasi-probabilities, which are an extended version of the standard probabilities used for describing the outcome of measurement for a single observable. The physical situations that require these quasi-probabilities arise when one considers quantum measurement of an observable conditioned by some other variable, with the notable example being the weak measurement employed to obtain Aharonov’s weak value. Specifically, we present a general prescription for the construction of
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Infusino, Maria, Salma Kuhlmann, Tobias Kuna, and Patrick Michalski. "Projective Limit Techniques for the Infinite Dimensional Moment Problem." Integral Equations and Operator Theory 94, no. 2 (2022). http://dx.doi.org/10.1007/s00020-022-02692-6.

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AbstractWe deal with the following general version of the classical moment problem: when can a linear functional on a unital commutative real algebra A be represented as an integral with respect to a Radon measure on the character space X(A) of A equipped with the Borel $$\sigma $$ σ -algebra generated by the weak topology? We approach this problem by constructing X(A) as a projective limit of the character spaces of all finitely generated unital subalgebras of A. Using some fundamental results for measures on projective limits of measurable spaces, we determine a criterion for the existence o
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Dissertations / Theses on the topic "Measurable Projection Theorem"

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Cotton, Michael R. "Determinacy in the Low Levels of the Projective Hierarchy." Miami University / OhioLINK, 2012. http://rave.ohiolink.edu/etdc/view?acc_num=miami1343245802.

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Books on the topic "Measurable Projection Theorem"

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Boudou, Alain, and Yves Romain. On Product Measures Associated with Stationary Processes. Edited by Frédéric Ferraty and Yves Romain. Oxford University Press, 2018. http://dx.doi.org/10.1093/oxfordhb/9780199568444.013.15.

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This article considers the connections between product measures and stationary processes. It first provides an overview of historical facts and relevant terminology, basic concepts and the mathematical approach. In particular, it discusses random measures, the projection-valued spectral measure (PVSM), convolution products, and the association between shift operators and PVSMs. It then presents the main results and their first potential applications, focusing on stochastic integrals, the image of a random measure under measurable mapping, the existence of a transport-type theorem, and the tran
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Book chapters on the topic "Measurable Projection Theorem"

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Garcia, Stephan Ramon, Javad Mashreghi, and William T. Ross. "Hilbert Spaces." In Operator Theory by Example. Oxford University PressOxford, 2023. http://dx.doi.org/10.1093/oso/9780192863867.003.0001.

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Abstract This chapter explores the basics of Hilbert spaces by using n-dimensional Euclidean space, he space of square-summable complex sequences, and the space of square-integrable, complex-valued Lebesgue-measurable function as examples. In addition, this chapter covers the Cauchy–Schwarz and triangle inequalities, orthonormal bases, and orthogonal projections. Since Banach spaces play a role in the subsequent chapters, this chapter also covers a few Banach-space basics.
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