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Zeitschriftenartikel zum Thema „Statistical equivalence“

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Autor: Grafiati

Veröffentlicht am 22. Juni 2024

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1

ÇAKI, Ahmet, und Aykut OR. „Asymptotically Lacunary statistical equivalent sequences in partial metric spaces“. Annals of Mathematics and Computer Science 22 (28.03.2024): 1–11. http://dx.doi.org/10.56947/amcs.v22.262.

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The present study deals with asymptotically equivalent sequences in partial metric spaces. We define the notions of strongly asymptotically lacunary equivalence, asymptotically statistical equivalence, and asymptotically lacunary statistical equivalence. We theoretically contribute to these notions and investigate some of their basic properties.

2

Lakens, Daniël. „Equivalence Tests“. Social Psychological and Personality Science 8, Nr. 4 (Mai 2017): 355–62. http://dx.doi.org/10.1177/1948550617697177.

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Scientists should be able to provide support for the absence of a meaningful effect. Currently, researchers often incorrectly conclude an effect is absent based a nonsignificant result. A widely recommended approach within a frequentist framework is to test for equivalence. In equivalence tests, such as the two one-sided tests (TOST) procedure discussed in this article, an upper and lower equivalence bound is specified based on the smallest effect size of interest. The TOST procedure can be used to statistically reject the presence of effects large enough to be considered worthwhile. This practical primer with accompanying spreadsheet and R package enables psychologists to easily perform equivalence tests (and power analyses) by setting equivalence bounds based on standardized effect sizes and provides recommendations to prespecify equivalence bounds. Extending your statistical tool kit with equivalence tests is an easy way to improve your statistical and theoretical inferences.

3

Goudra, BasavanaG, und PreetMohinder Singh. „Clinical perspective on statistical equivalence“. Journal of Anaesthesiology Clinical Pharmacology 29, Nr. 4 (2013): 457. http://dx.doi.org/10.4103/0970-9185.119130.

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4

Lavenda, B. H. „Statistical Equivalence and Particle Indistinguishability“. Physics Essays 5, Nr. 2 (Juni 1992): 206–14. http://dx.doi.org/10.4006/1.3028972.

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5

Lazar, Nicole. „Testing Statistical Hypotheses of Equivalence“. Technometrics 45, Nr. 3 (August 2003): 271–72. http://dx.doi.org/10.1198/tech.2003.s775.

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6

Munk, Axel. „Testing Statistical Hypotheses of Equivalence“. Journal of the American Statistical Association 99, Nr. 465 (März 2004): 293. http://dx.doi.org/10.1198/jasa.2004.s317.

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7

Gutkin, Eugene. „Equivalence principle in statistical mechanics“. Physica A: Statistical Mechanics and its Applications 144, Nr. 2-3 (August 1987): 430–44. http://dx.doi.org/10.1016/0378-4371(87)90200-7.

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8

Röhmel, Joachim. „Therapeutic equivalence investigations: statistical considerations“. Statistics in Medicine 17, Nr. 15-16 (15.08.1998): 1703–14. http://dx.doi.org/10.1002/(sici)1097-0258(19980815/30)17:15/16<1703::aid-sim972>3.0.co;2-g.

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9

Edely, O. H., und M. Mursaleen. „On $A$-statistical convergence and $A$-statistical Cauchy via idea“. Carpathian Mathematical Publications 14, Nr. 2 (30.12.2022): 442–52. http://dx.doi.org/10.15330/cmp.14.2.442-452.

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In [Analysis 1985, 5 (4), 301-313], J.A. Fridy proved an equivalence relation between statistical convergence and statistical Cauchy sequence. In this paper, we define $A^{I^{\ast }}$-statistical convergence and find under certain conditions, that it is equivalent to $A^{I}$-statistical convergence defined in [Appl. Math. Lett. 2012, 25 (4), 733-738]. Moreover, we define $A^{I}$- and $A^{I^{\ast }}$-statistical Cauchy sequences and find some equivalent relation with $A^{I}$- and $A^{I^{\ast }}$-statistical convergence.

10

Koşar, Cem, Mehmet Küçükaslan und Mikail Et. „On asymptotically deferred statistical equivalence of sequences“. Filomat 31, Nr. 16 (2017): 5139–50. http://dx.doi.org/10.2298/fil1716139k.

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In this study, combining the definition of asymptotically equivalence of sequences and deferred density, the concepts of asymptotically deferred statistical equivalence and strong deferred asymptotically equivalence of nonnegative sequences are introduced. Besides, the main properties of asymptotically deferred statistical equivalence and strong deferred asymptotically equivalence, some inclusion and equivalence results are given.

11

Markus, Keith A. „Statistical Equivalence, Semantic Equivalence, Eliminative Induction, and the Raykov-Marcoulides Proof of Infinite Equivalence“. Structural Equation Modeling: A Multidisciplinary Journal 9, Nr. 4 (Oktober 2002): 503–22. http://dx.doi.org/10.1207/s15328007sem0904_3.

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12

Kim, Taehwa, und Jinsook Kim. „Analysis of Equivalence and Reliability of Korean Translated Abbreviated Profile of Hearing Aid Benefits“. Audiology and Speech Research 16, Nr. 3 (31.07.2020): 175–87. http://dx.doi.org/10.21848/asr.200025.

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For using the translated questionnaires, an appropriate translation should be accomplished for establishing the equivalence. The equivalence is divided into two categories, formal equivalence regarding words and grammar and dynamic equivalence meaning the naturalness of the context with the consideration of the cultural and emotional characteristics of the region. The purpose of this study was to verify formal and dynamic equivalences and statistical reliability of the widely used translated questionnaire in Korea, abbreviated profile of hearing aid benefits (APHAB). The identification of equivalence was conducted in formal and dynamic categories and the statistical verification was performed for 6 translated APHAB which are currently utilized in Korea. None of 6 translated APHAB had formal and dynamic equivalences for all 24 items when the score ‘2’ was given to the completed equivalence of each item. Two translated APHAB showed ‘11’ as the best score and one of them showed ‘0’ for the formal equivalence identification. For the dynamic equivalence, the two translated APHAB scored ‘20’ as the best score. The one scored ‘0’ for the formal equivalence showed ‘0’ also in the dynamic equivalence. And only two translated APHAB presented the statistical validation using Cronbach’s alpha and factor analysis. It was confirmed that any of 6 translated APHAB in Korea could not reproduce the original contents with the appropriate equivalence and statistical validation. As the translated version was found to have a limitation in delivering the original contents due to language, emotional and cultural differences, a Korean questionnaire should be developed.

13

O’Brien, Myles W., und Derek S. Kimmerly. „Is “not different” enough to conclude similar cardiovascular responses across sexes?“ American Journal of Physiology-Heart and Circulatory Physiology 322, Nr. 3 (01.03.2022): H355—H358. http://dx.doi.org/10.1152/ajpheart.00687.2021.

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The number of research studies investigating whether similar or different cardiovascular responses or adaptations exist between males and females is increasing. Traditionally, difference-based statistical methods, e.g., t test, ANOVA, etc., have been implemented to compare cardiovascular function between males and females, with a P value of >0.05 used to denote similarity between sexes. However, an absence of evidence, i.e., large P value, is not evidence of absence, i.e., no sex differences. Equivalence testing determines whether two measures or groups provide statistically equivalent outcomes, in that they differ by less than an “ideally prespecified” smallest effect size of interest. Our perspective discusses the applicability and utility of integrating equivalence testing when conducting sex comparisons in cardiovascular research. An emphasis is placed on how cardiovascular researchers may conduct equivalence testing across multiple study designs, e.g., cross-sectional comparisons, repeated-measures intervention, etc. The strengths and weaknesses of this statistical tool are discussed. Equivalence analyses are relatively simple to conduct, may be used in conjunction with traditional hypothesis testing to interpret findings, and permit the determination of statistically equivalent responses between sexes. We recommend that cardiovascular researchers consider implementing equivalence testing to better our understanding of similar and different cardiovascular processes between sexes.

14

Mau, Jochen. „A statistical assessment of clinical equivalence“. Statistics in Medicine 7, Nr. 12 (Dezember 1988): 1267–77. http://dx.doi.org/10.1002/sim.4780071207.

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15

O’Brien, Myles W. „Implications and Recommendations for Equivalence Testing in Measures of Movement Behaviors: A Scoping Review“. Journal for the Measurement of Physical Behaviour 4, Nr. 4 (01.12.2021): 353–62. http://dx.doi.org/10.1123/jmpb.2021-0021.

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Equivalence testing may provide complementary information to more frequently used statistical procedures because it determines whether physical behavior outcomes are statistically equivalent to criterion measures. A caveat of this procedure is the predetermined selection of upper and lower bounds of acceptable error around a specified zone of equivalence. With no clear guidelines available to assist researchers, these equivalence zones are arbitrarily selected. A scoping review of articles implementing equivalence testing was performed to determine the validity of physical behavior outcomes; the aim was to characterize how this procedure has been implemented and to provide recommendations. A literature search from five databases initially identified potentially 1,153 articles which resulted in the acceptance of 19 studies (20 arms) conducted in children/youth and 40 in adults (49 arms). Most studies were conducted in free-living conditions (children/youth = 13 arms; adults = 22 arms) and employed a ±10% equivalence zone. However, equivalence zones ranged from ±3% to ±25% with only a subset using absolute thresholds (e.g., ±1,000 steps/day). If these equivalence zones were increased or decreased by ±5%, 75% (15/20, children/youth) and 71% (35/49, adults), they would have exhibited opposing equivalence test outcomes (i.e., equivalent to nonequivalent or vice versa). This scoping review identifies the heterogeneous usage of equivalence testing in studies examining the accuracy of (in)activity measures. In the absence of evidence-based standardized equivalence criteria, presenting the percentage required to achieve statistical equivalence or using absolute thresholds as a proportion of the SD may be a better practice than arbitrarily selecting zones a priori.

16

Konca, Şukran. „Asymptotically deferred f-statistical equivalence of sequences“. Filomat 32, Nr. 16 (2018): 5585–93. http://dx.doi.org/10.2298/fil1816585k.

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In this work, we obtain a generalization of asymptotically deferred statistical equivalence of non-negative real-valued sequences with the aid of a modulus function. Further, we examine some of main properties of asymptotically deferred f-statistical equivalence and obtain some equivalence results and inclusion relations.

17

Kışı, Ömer, und Fatıh Nuray. „On -Asymptotically Statistical Equivalence of Sequences of Sets“. ISRN Mathematical Analysis 2013 (15.09.2013): 1–6. http://dx.doi.org/10.1155/2013/602963.

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This paper presents the notion of -asymptotically statistical equivalence, which is a natural combination of asymptotic -equivalence, and -statistical equivalence for sequences of sets. We find its relations to -asymptotically statistical convergence, strong -asymptotically equivalence, and strong Cesaro -asymptotically equivalence for sequences of sets.

18

Ulusu, Uğur, und Fatih Nuray. „On Asymptotically Lacunary Statistical Equivalent Set Sequences“. Journal of Mathematics 2013 (2013): 1–5. http://dx.doi.org/10.1155/2013/310438.

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This paper presents three definitions which are natural combination of the definitions of asymptotic equivalence, statistical convergence, lacunary statistical convergence, and Wijsman convergence. In addition, we also present asymptotically equivalent (Wijsman sense) analogs of theorems in Patterson and Savaş (2006).

19

Hazarika, Bipan. „Wijsman Orlicz Asymptotically Ideal -Statistical Equivalent Sequences“. Journal of Function Spaces and Applications 2013 (2013): 1–9. http://dx.doi.org/10.1155/2013/257181.

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An ideal is a family of subsets of positive integers which is closed under taking finite unions and subsets of its elements. In this paper, we introduce a new definition of asymptotically ideal -statistical equivalent sequence in Wijsman sense and present some definitions which are the natural combination of the definition of asymptotic equivalence, statistical equivalent, -statistical equivalent sequences in Wijsman sense. Finally, we introduce the notion of Cesaro Orlicz asymptotically -equivalent sequences in Wijsman sense and establish their relationship with other classes.

20

Macci, Claudio. „The "statistical experiment"-equivalence for prior distributions“. Bulletin of the Belgian Mathematical Society - Simon Stevin 5, Nr. 5 (1998): 649–64. http://dx.doi.org/10.36045/bbms/1103211557.

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21

Pardoe, Heath R., Gary R. Cutter, Rachel Alter, Rebecca Kucharsky Hiess, Mira Semmelroch, Donna Parker, Shawna Farquharson, Graeme D. Jackson und Ruben Kuzniecky. „Pooling Morphometric Estimates: A Statistical Equivalence Approach“. Journal of Neuroimaging 26, Nr. 1 (21.06.2015): 109–15. http://dx.doi.org/10.1111/jon.12265.

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22

Limentani, Giselle B., Moira C. Ringo, Feng Ye, Mandy L. Bergquist und Ellen O. MCSorley. „Beyond the t-Test: Statistical Equivalence Testing“. Analytical Chemistry 77, Nr. 11 (Juni 2005): 221 A—226 A. http://dx.doi.org/10.1021/ac053390m.

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23

Llabrés, Matı́as, Alexis Oliva und José Fariña. „Statistical assessment of between batch stability equivalence“. International Journal of Pharmaceutics 204, Nr. 1-2 (Juni 2000): 61–68. http://dx.doi.org/10.1016/s0378-5173(00)00469-5.

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24

Dalalyan, Arnak, und Markus Reiß. „Asymptotic statistical equivalence for scalar ergodic diffusions“. Probability Theory and Related Fields 134, Nr. 2 (03.05.2005): 248–82. http://dx.doi.org/10.1007/s00440-004-0416-1.

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25

Alvir, Jose Ma J. „P41 Equivalence testing using available statistical software“. Controlled Clinical Trials 14, Nr. 5 (Oktober 1993): 444. http://dx.doi.org/10.1016/0197-2456(93)90173-b.

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26

Schall, Robert. „Book Review: Testing statistical hypotheses of equivalence“. Clinical Trials: Journal of the Society for Clinical Trials 1, Nr. 1 (Februar 2004): 139–40. http://dx.doi.org/10.1191/1740774504cn012xx.

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27

Uohashi, Keiko. „On \alpha -conformal equivalence of statistical submanifolds“. Journal of Geometry 75, Nr. 1-2 (01.12.2002): 179–84. http://dx.doi.org/10.1007/s00022-022-1463-3.

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28

Albright, Leif, Kenneth F. Reeve, Sharon A. Reeve und April N. Kisamore. „Teaching statistical variability with equivalence-based instruction“. Journal of Applied Behavior Analysis 48, Nr. 4 (22.09.2015): 883–94. http://dx.doi.org/10.1002/jaba.249.

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29

Ulusu, Uǧur. „Asymptotically ideal invariant equivalence“. Creative Mathematics and Informatics 27, Nr. 2 (2018): 215–20. http://dx.doi.org/10.37193/cmi.2018.02.14.

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In this paper, the concepts of asymptotically \mathcal{I}_{\sigma}-equivalence, \sigma-asymptotically equivalence, st\-rong\-ly \sigma-asymptotically equivalence and strongly \sigma-asymptotically p-equivalence for real number sequences are de\-fi\-ned. Also, we give relationships among these new type equivalence concepts and the concept of \linebreak S_{\sigma}-asymptotically equivalence which is studied in [Savaş, E. and Patterson, R. F., \sigma-asymptotically lacunary statistical equivalent sequences, Cent. Eur. J. Math., 4 (2006), No. 4, 648–655].

30

López, M. C., R. J. Noriega und C. G. Schifini. „Equivalence ands‐equivalence of vector‐tensor Lagrangians“. Journal of Mathematical Physics 32, Nr. 8 (August 1991): 2063–64. http://dx.doi.org/10.1063/1.529227.

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31

Cho, Youngkyu, Jeongho Lee, Taehyun Yun, Yongmin Jo, Seonwoo Oh und Yongsung Joo. „Safety Assessment of Genetically Modified Rice Based on Substantial Equivalence“. Korean Data Analysis Society 25, Nr. 6 (31.12.2023): 2143–57. http://dx.doi.org/10.37727/jkdas.2023.25.6.2143.

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Genetically modified crops must undergo safety evaluation approval before commercial use, ensuring substantial equivalence compared to conventional crops. Safety assessment based on 'substantial equivalence' involves a stepwise approach, comparing GM crops with their non-GM counterparts, examining statistical differences or equivalence within the natural variability range for the desired attributes. For instance, if statistically significant differences are observed in safety test items between GM and control crops, additional analysis compares them to the commercially available varieties to determine inclusion within their compositional range. Further analysis involves biological or toxicological assessments if difference between GM crops and others are identified. Using data from insect-resistant genetically modified rice and its non-GM counterpart, available in the Rural Development Administration's crop component database, we applied statistical methods for substantial equivalence assessment. The substantial equivalence assessment of GM crops covers various evaluation aspects, including toxicological, allergenic, and nutritional attributes. In this study, statistical analysis was performed on rice's nutritional component data, integrating the results with theoretical contents.

32

Govinder, K. S. „On the equivalence of ‘non-equivalent’ algebraic realizations“. Journal of Physics A: Mathematical and Theoretical 40, Nr. 29 (03.07.2007): 8363–69. http://dx.doi.org/10.1088/1751-8113/40/29/011.

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33

Gülle, Esra. „Double Wijsman asymptotically statistical equivalence of order α“. Journal of Intelligent & Fuzzy Systems 38, Nr. 2 (06.02.2020): 2081–87. http://dx.doi.org/10.3233/jifs-190796.

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34

ULUSU, Uğur, Erdinç DÜNDAR und Nimet PANCAROĞLU AKIN. „Lacunary invariant statistical equivalence for double set sequences“. Communications Faculty Of Science University of Ankara Series A1Mathematics and Statistics 71, Nr. 1 (31.03.2022): 1–12. http://dx.doi.org/10.31801/cfsuasmas.903988.

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35

KUNCHEVA, LUDMILA I. „ON THE EQUIVALENCE BETWEEN FUZZY AND STATISTICAL CLASSIFIERS“. International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems 04, Nr. 03 (Juni 1996): 245–53. http://dx.doi.org/10.1142/s0218488596000159.

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In this paper the equivalence between fuzzy systems and two nonparametric techniques for pattern recognition is considered. The conditions under which a fuzzy system coincides with the nearest neighbor rule, and with the Parzen’s classifier have been formulated.

36

Casetti, Lapo, und Michael Kastner. „Partial equivalence of statistical ensembles and kinetic energy“. Physica A: Statistical Mechanics and its Applications 384, Nr. 2 (Oktober 2007): 318–34. http://dx.doi.org/10.1016/j.physa.2007.05.043.

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37

Görgen, Christiane, Anna Bigatti, Eva Riccomagno und Jim Q. Smith. „Discovery of statistical equivalence classes using computer algebra“. International Journal of Approximate Reasoning 95 (April 2018): 167–84. http://dx.doi.org/10.1016/j.ijar.2018.01.003.

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38

Gujrati, Purushottam. „On Equivalence of Nonequilibrium Thermodynamic and Statistical Entropies“. Entropy 17, Nr. 2 (05.02.2015): 710–54. http://dx.doi.org/10.3390/e17020710.

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39

Sajfert, Vjekoslav, Stevo Jácimovski, Dušan Popov und Bratislav Tošić. „Statistical and Dynamical Equivalence of Different Elementary Cells“. Journal of Computational and Theoretical Nanoscience 4, Nr. 3 (01.05.2007): 619–26. http://dx.doi.org/10.1166/jctn.2007.025.

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40

Garbe, E., J. R�hmel und U. Gundert-Remy. „Clinical and statistical issues in therapeutic equivalence trials“. European Journal of Clinical Pharmacology 45, Nr. 1 (August 1993): 1–7. http://dx.doi.org/10.1007/bf00315342.

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41

Hatch, John P. „Using statistical equivalence testing in clinical biofeedback research“. Biofeedback and Self-Regulation 21, Nr. 2 (Juni 1996): 105–19. http://dx.doi.org/10.1007/bf02284690.

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42

Furuuchi, Kazuyuki. „Equivalence of Projections as Gauge Equivalence¶on Noncommutative Space“. Communications in Mathematical Physics 217, Nr. 3 (März 2001): 579–93. http://dx.doi.org/10.1007/pl00005554.

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43

Casabianca, Jodi M., und Charles Lewis. „Statistical Equivalence Testing Approaches for Mantel–Haenszel DIF Analysis“. Journal of Educational and Behavioral Statistics 43, Nr. 4 (01.12.2017): 407–39. http://dx.doi.org/10.3102/1076998617742410.

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The null hypothesis test used in differential item functioning (DIF) detection tests for a subgroup difference in item-level performance—if the null hypothesis of “no DIF” is rejected, the item is flagged for DIF. Conversely, an item is kept in the test form if there is insufficient evidence of DIF. We present frequentist and empirical Bayes approaches for implementing statistical equivalence testing for DIF using the Mantel–Haenszel (MH) DIF statistic. With these approaches, rejection of the null hypothesis of “DIF” allows the conclusion of statistical equivalence, a more stringent criterion for keeping items. In other words, the roles of the null and alternative hypotheses are interchanged in order to have positive evidence that the DIF of an item is small. A simulation study compares the equivalence testing approaches to the traditional MH DIF detection method with the Educational Testing Service classification system. We illustrate the methods with item response data from the 2012 Programme for International Student Assessment.

44

Hazarika, Bipan, und Ayhan Esi. „On asymptotically Wijsman lacunary statistical convergence of set sequences in ideal context“. Filomat 31, Nr. 9 (2017): 2691–703. http://dx.doi.org/10.2298/fil1709691h.

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In this paper, we introduce some definitions which are natural combination of the notions of asymptotic equivalence, statistical convergence, lacunary statistical convergence, Wijsman convergence and ideal. In addition, we also define the concept of asymptotically equivalent sequences of sets in the sense ofWijsman convergence and prove some interesting results related to these concepts.

45

VAHL, C. I., und Q. KANG. „Equivalence criteria for the safety evaluation of a genetically modified crop: a statistical perspective“. Journal of Agricultural Science 154, Nr. 3 (08.04.2015): 383–406. http://dx.doi.org/10.1017/s0021859615000271.

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SUMMARYSafety evaluation of a genetically modified (GM) crop is accomplished by establishing its substantial equivalence to non-GM reference crops with a history of safe use. Testing hypotheses of equivalence rather than difference is the appropriate statistical approach. A necessary first step in this regard is to specify a reasonable equivalence criterion that includes a measure for discrepancy between the GM and reference crops as well as a regulatory threshold. The present work explored several equivalence criteria and discussed their pros and cons. Each criterion addresses one of three ordered classes of equivalence: super, conditional and marginal equivalence. Their implications were investigated over an array of parameter values estimated from a real-world dataset. Marginal equivalence was identified as adhering most closely to the concept of substantial equivalence. Because conditional equivalence logically implies marginal equivalence and is practically quantifiable from current field designs, the present work recommends conditional equivalence criteria while encouraging producers to improve their design to enable testing marginal equivalence in the future. Contrary to concerns of the ag-biotech industry, empirical evidence from recent publications indicates that a linear mixed model currently implemented by the European Food Safety Authority is adequate for assessing equivalence despite its lack of genotype-by-environment interaction terms.

46

Gümüş, Hafi̇ze, und Nihal Demir. „A New Type of Generalization on W—Asymptotically Jλ—Statistical Equivalence with the Number of α“. Axioms 7, Nr. 3 (02.08.2018): 54. http://dx.doi.org/10.3390/axioms7030054.

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In our paper, by using the concept of W-asymptotically J- statistical equivalence of order α which has been previously defined, we present the definitions of W-asymptotically Jλ-statistical equivalence of order α, W-strongly asymptotically Jλ-statistical equivalence of order α, and W-strongly Cesáro asymptotically J-statistical equivalence of order α where 0<α≤1. We also extend these notions with a sequence of positive real numbers, p=(pk), and we investigate how our results change if p is constant.

47

Turan, Ceylan, und Oktay Duman. „Fundamental properties of statistical convergence and lacunary statistical convergence on time scales“. Filomat 31, Nr. 14 (2017): 4455–67. http://dx.doi.org/10.2298/fil1714455t.

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In this paper, we first obtain a Tauberian condition for statistical convergence on time scales. We also find necessary and sufficient conditions for the equivalence of statistical convergence and lacunary statistical convergence on time scales. Some significant applications are also presented.

48

Alkan, Meryem Ece, und Fatih Nuray. „Strongly deferred almost convergence and deferred almost statistical convergence“. MATHEMATICA 64 (87), Nr. 2 (15.12.2022): 151–63. http://dx.doi.org/10.24193/mathcluj.2022.2.01.

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This paper introduces the concepts of deferred almost convergence, strongly deferred almost convergence and deferred almost statistical convergence, and investigates the relationship between these concepts. Also, it gives the notions of asymptotical deferred almost equivalence and asymptotical deferred almost statistical equivalence.

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Hazarika, Bipan, und Ayhan Esi. „ON λ-ASYMPTOTICALLY WIJSMAN GENERALIZED STATISTICAL CONVERGENCE OF SEQUENCES OF SETS“. Tatra Mountains Mathematical Publications 56, Nr. 1 (01.11.2013): 67–77. http://dx.doi.org/10.2478/tmmp-2013-0025.

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ABSTRACT The concept of Wijsman statistical convergence was defined by [Nuray, F.-Rhoades, B. E.: Statistical convergence of sequences of sets, Fasc. Math. 49 (2012), 1-9]. In this paper we present three definitions which are a natural combination of the definition of asymptotic equivalence, statistical convergence, generalized statistical convergence and Wijsman convergence. In addition, we also present asymptotically equivalent sequences of sets in sense of Wijsman and study some properties of this concept.

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Logunov, A. A., M. A. Mestvirishvili und Yu V. Chugreev. „The equivalence principle“. Theoretical and Mathematical Physics 99, Nr. 1 (April 1994): 470–83. http://dx.doi.org/10.1007/bf01018801.

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