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Journal articles on the topic 'Measure theory'

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Published: 4 June 2021
Last updated: 29 July 2024

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1

O'Brien, Katharine. "Measure Theory." Mathematics Magazine 58, no. 1 (January 1, 1985): 23. http://dx.doi.org/10.2307/2690232.

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2

Applebaum, Dave, and Donald L. Cohn. "Measure Theory." Mathematical Gazette 79, no. 484 (March 1995): 222. http://dx.doi.org/10.2307/3620102.

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3

Rosalsky, Andrew, and J. L. Doob. "Measure Theory." Journal of the American Statistical Association 89, no. 428 (December 1994): 1566. http://dx.doi.org/10.2307/2291029.

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4

O'Brien, Katharine. "Measure Theory." Mathematics Magazine 58, no. 1 (January 1985): 23. http://dx.doi.org/10.1080/0025570x.1985.11977142.

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5

Kiessler, Peter C. "Measure Theory and Probability Theory." Journal of the American Statistical Association 102, no. 479 (September 2007): 1078. http://dx.doi.org/10.1198/jasa.2007.s207.

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6

Harrison, Flona. "Measure for measure in quantum theory." Physics World 9, no. 3 (March 1996): 24–25. http://dx.doi.org/10.1088/2058-7058/9/3/22.

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7

Weihrauch, Klaus. "Computable Measure Theory." Electronic Proceedings in Theoretical Computer Science 24 (June 3, 2010): 4. http://dx.doi.org/10.4204/eptcs.24.4.

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8

Clarke, L. E., Malcolm Adams, and Victor Guillemin. "Measure Theory and Probability." Mathematical Gazette 71, no. 455 (March 1987): 80. http://dx.doi.org/10.2307/3616316.

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9

Rosalsky, Andrew, Malcolm Adams, and Victor Guillemin. "Measure Theory and Probability." Journal of the American Statistical Association 82, no. 398 (June 1987): 700. http://dx.doi.org/10.2307/2289512.

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10

RL, Malcolm Adams, and Victor Guillemin. "Measure Theory and Probability." Journal of the American Statistical Association 91, no. 436 (December 1996): 1754. http://dx.doi.org/10.2307/2291614.

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11

Meyer, P. A. "Book Review: Measure theory." Bulletin of the American Mathematical Society 31, no. 2 (October 1, 1994): 233–36. http://dx.doi.org/10.1090/s0273-0979-1994-00541-5.

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12

Yu-Zhen, Dong, and Chen Huan. "Credibility Measure Theory Analysis." Procedia Engineering 15 (2011): 1722–26. http://dx.doi.org/10.1016/j.proeng.2011.08.321.

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13

Bao, Lingxin, and Lixin Cheng. "On statistical measure theory." Journal of Mathematical Analysis and Applications 407, no. 2 (November 2013): 413–24. http://dx.doi.org/10.1016/j.jmaa.2013.05.039.

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14

Aldaz, J. M., and P. A. Loeb. "Counterexamples in Nonstandard Measure Theory." Canadian Mathematical Bulletin 38, no. 3 (September 1, 1995): 257–61. http://dx.doi.org/10.4153/cmb-1995-038-5.

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15

Nillsen, Rodney. "Normal Numbers without Measure Theory." American Mathematical Monthly 107, no. 7 (August 2000): 639. http://dx.doi.org/10.2307/2589120.

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16

Kharazishvili, A. "Some problems in measure theory." Colloquium Mathematicum 62, no. 2 (1991): 197–220. http://dx.doi.org/10.4064/cm-62-2-197-220.

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17

Toro, Tatiana. "Geometric Measure Theory–Recent Applications." Notices of the American Mathematical Society 66, no. 04 (April 1, 2019): 1. http://dx.doi.org/10.1090/noti1853.

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18

Gudder, Stan. "Quantum measure and integration theory." Journal of Mathematical Physics 50, no. 12 (December 2009): 123509. http://dx.doi.org/10.1063/1.3267867.

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19

HENRY, SIMON. "Measure theory over boolean toposes." Mathematical Proceedings of the Cambridge Philosophical Society 163, no. 1 (August 30, 2016): 1–21. http://dx.doi.org/10.1017/s0305004116000700.

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AbstractIn this paper we develop a notion of measure theory over boolean toposes reminiscent of the theory of von Neumann algebras. This is part of a larger project to study relations between topos theory and noncommutative geometry. The main result is a topos theoretic version of the modular time evolution of von Neumann algebras which take the form of a canonical $\mathbb{R}^{>0}$-principal bundle over any integrable locally separated boolean topos.
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20

Cheng, LiXin, GuoChen Lin, YongYi Lan, and Hui Liu. "Measure theory of statistical convergence." Science in China Series A: Mathematics 51, no. 12 (September 23, 2008): 2285–303. http://dx.doi.org/10.1007/s11425-008-0017-z.

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21

Nillsen, Rodney. "Normal Numbers Without Measure Theory." American Mathematical Monthly 107, no. 7 (August 2000): 639–44. http://dx.doi.org/10.1080/00029890.2000.12005250.

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22

Ciurea, Grigore. "Nonstandard Methods in Measure Theory." Abstract and Applied Analysis 2014 (2014): 1–10. http://dx.doi.org/10.1155/2014/851080.

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Ideas and techniques from standard and nonstandard theories of measure spaces and Banach spaces are brought together to give a new approach to the study of the extension of vector measures. Applications of our results lead to simple new proofs for theorems of classical measure theory. The novelty lies in the use of the principle of extension by continuity (for which we give a nonstandard proof) to obtain in an unified way some notable theorems which have been obtained by Fox, Brooks, Ohba, Diestel, and others. The methods of proof are quite different from those used by previous authors, and most of them are realized by means of nonstandard analysis.
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23

Kohout, L. J. "Fuzzy Measure Theory [Book Reviews]." IEEE Transactions on Fuzzy Systems 3, no. 4 (November 1995): 480. http://dx.doi.org/10.1109/tfuzz.1995.481959.

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24

Kirchheim, B. "Seminar on geometric measure theory." Acta Applicandae Mathematicae 23, no. 1 (April 1991): 95–101. http://dx.doi.org/10.1007/bf00046922.

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25

Smirnov, A. G., and M. S. Smirnov. "Completion Procedures in Measure Theory." Analysis Mathematica 49, no. 3 (September 2023): 855–80. http://dx.doi.org/10.1007/s10476-023-0233-3.

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26

Bezushchak, O. O., and B. V. Oliynyk. "Algebraic theory of measure algebras." Reports of the National Academy of Sciences of Ukraine, no. 2 (May 3, 2023): 3–9. http://dx.doi.org/10.15407/dopovidi2023.02.003.

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A. Horn and A. Tarski initiated the abstract theory of measure algebras. Independently V. Sushchansky, B. Oliynyk and P. Cameron studied the direct limits of Hamming spaces. In the current paper, we introduce new examples of locally standard measure algebras and complete the classification of countable locally standard measure algebras. Countable unital locally standard measure algebras are in one-to-one correspondence with Steinitz numbers. Given a Steinitz number s such measure algebra is isomorphic to the Boolean algebra of s-periodic sequences of 0 and 1. Nonunital locally standard measure algebras are parametrized by pairs (s, r), where s is a Steinitz number and r is a real number greater or equal to 1. We also show that an arbitrary (not necessarily locally standard) measure algebra is embeddable in a metric ultraproduct of standard Hamming spaces. In other words, an arbitrary measure algebra is sofic.
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27

Vulfs, T. O., and E. I. Guendelman. "Galileon string measure and other modified measure extended objects." Modern Physics Letters A 32, no. 38 (December 14, 2017): 1750211. http://dx.doi.org/10.1142/s021773231750211x.

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We show that it is possible to formulate string theory as a “Galileon string theory”. The Galileon field [Formula: see text] enters in the definition of the integration measure in the action. Following the methods of the modified measure string theory, we find that the final equations are again those of the sigma-model. Moreover, the string tension appears again as an additional dynamical degree of freedom. At the same time, the theory satisfies all requirements of the Galileon higher derivative theory at the action level while the equations of motion are still of the second-order. A Galileon symmetry is displayed explicitly in the conformal string worldsheet frame. Also, we define the Galileon gauge transformations. Generalizations to branes with other modified measures are discussed.
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28

Luo, Shi Hua. "The Structure of Fuzzifying Measure Space and Fuzzifying Measure." Advanced Materials Research 108-111 (May 2010): 844–49. http://dx.doi.org/10.4028/www.scientific.net/amr.108-111.844.

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A new so-called fuzzifying measurable theory that generalizes the classical measurable theory is established, the essence of which is a fuzzy measure on a multiple-valued algebra. First, the semantics method of continuous-valued logic is used to describe the new measure succinctly. Then, the structures of the new theory are discussed in detail and some of the key structural features of the classic measure can be successfully extended to the new theory. Lastly, the product of the two fuzzifying measures is studied and a problem, which is similar to the third of the open problems in fuzzy measure by Z. Wang, is considered.
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29

Nicolaescu, Mădălina, and Oana-Alis Zaharia. "Measure for Measure." Cahiers Élisabéthains: A Journal of English Renaissance Studies 103, no. 1 (November 2020): 168–72. http://dx.doi.org/10.1177/0184767820946175u.

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30

Ludot-Vlasak, Ronan, Edouard Marsoin, and Cécile Roudeau. "‘The measure! The measure!’." Textual Practice 35, no. 11 (November 2, 2021): 1727–32. http://dx.doi.org/10.1080/0950236x.2021.1984082.

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31

Rappaport, Gideon. "Measuring Measure for Measure." Renascence 39, no. 4 (1987): 502–13. http://dx.doi.org/10.5840/renascence198739410.

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32

He, Hujun, Chong Tian, Gang Jin, and Le An. "An Improved Uncertainty Measure Theory Based on Game Theory Weighting." Mathematical Problems in Engineering 2019 (May 27, 2019): 1–8. http://dx.doi.org/10.1155/2019/3893129.

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In the application of uncertainty measure theory, the determination method of index weight mainly includes the subjective weight determination method and the objective weight determination method. The subjective weight determination method has the disadvantages affected by the subjective preference of the decision-maker. The objective weight determination method often ignores the participation degree of the decision-maker, and when using the uncertainty measure evaluation model to perform multi-index classification evaluation, the credible degree recognition criterion is often used as the attribute recognition of the object to be measured, because the credible degree is taken by the subjective people, and the different values of different people have a great influence on the evaluation results. In order to solve the above problems in the uncertainty measure theory, this paper used the combination weighting of game theory to determine the optimal weight. At the same time, the credible degree recognition criterion was improved on the basis of the concept of minimum uncertainty measure distance, and a game theory-improved uncertainty measure optimization model was proposed. Finally, the validity of the model was proven by a case.
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33

Liu, Fangda, and Ruodu Wang. "A Theory for Measures of Tail Risk." Mathematics of Operations Research 46, no. 3 (August 2021): 1109–28. http://dx.doi.org/10.1287/moor.2020.1072.

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The notion of “tail risk” has been a crucial consideration in modern risk management and financial regulation, as very well documented in the recent regulatory documents. To achieve a comprehensive understanding of the tail risk, we carry out an axiomatic study for risk measures that quantify the tail risk, that is, the behaviour of a risk beyond a certain quantile. Such risk measures are referred to as tail risk measures in this paper. The two popular classes of regulatory risk measures in banking and insurance, value at risk (VaR) and expected shortfall, are prominent, yet elementary, examples of tail risk measures. We establish a connection between a tail risk measure and a corresponding law-invariant risk measure, called its generator, and investigate their joint properties. A tail risk measure inherits many properties from its generator, but not subadditivity or convexity; nevertheless, a tail risk measure is coherent if and only if its generator is coherent. We explore further relevant issues on tail risk measures, such as bounds, distortion risk measures, risk aggregation, elicitability, and dual representations. In particular, there is no elicitable tail convex risk measure other than the essential supremum, and under a continuity condition, the only elicitable and positively homogeneous monetary tail risk measures are the VaRs.
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34

Hadfield, Andrew. "Shakespeare's Measure for Measure." Explicator 61, no. 2 (January 2003): 71–73. http://dx.doi.org/10.1080/00144940309597759.

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35

Blythe, David-Everett. "Shakespeare's MEASURE FOR MEASURE." Explicator 58, no. 1 (January 1999): 4–6. http://dx.doi.org/10.1080/00144949909596986.

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36

Mustazza, Leonard. "Shakespeare's Measure for Measure." Explicator 47, no. 1 (September 1988): 2–4. http://dx.doi.org/10.1080/00144940.1988.9933859.

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37

SUGENO, Michio, and Toshiaki MUROFUSHI. "An Introduction to Fuzzy Measure Theory." Journal of Japan Society for Fuzzy Theory and Systems 2, no. 2 (1990): 174–81. http://dx.doi.org/10.3156/jfuzzy.2.2_174.

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38

SUGENO, Michio, and Toshiaki MUROFUSHI. "An Introduction to Fuzzy Measure Theory." Journal of Japan Society for Fuzzy Theory and Systems 2, no. 3 (1990): 370–81. http://dx.doi.org/10.3156/jfuzzy.2.3_370.

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39

Daele, A. Van. "The Lebesgue Integral Without Measure Theory." American Mathematical Monthly 97, no. 10 (December 1990): 912. http://dx.doi.org/10.2307/2324331.

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40

Almgren, Frederick J., and Frank Morgan. "Geometric Measure Theory. A Beginner's Guide." American Mathematical Monthly 96, no. 8 (October 1989): 753. http://dx.doi.org/10.2307/2324741.

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41

Abért, Miklós, Damien Gaboriau, and Andreas Thom. "Group Theory, Measure, and Asymptotic Invariants." Oberwolfach Reports 10, no. 3 (2013): 2375–422. http://dx.doi.org/10.4171/owr/2013/42.

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42

De Lellis, Camillo, Guido De Philippis, Bernd Kirchheim, and Riccardo Tione. "Geometric measure theory and differential inclusions." Annales de la Faculté des sciences de Toulouse : Mathématiques 30, no. 4 (December 6, 2021): 899–960. http://dx.doi.org/10.5802/afst.1691.

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43

Zhang, Shao Pu, and Tao Feng. "Uncertainty Measure Based on Evidence Theory." Applied Mechanics and Materials 329 (June 2013): 344–48. http://dx.doi.org/10.4028/www.scientific.net/amm.329.344.

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Evidence theory is an effective method to deal with uncertainty information. And uncertainty measure is to reflect the uncertainty of an information system. Thus we want to merge evidence theory with uncertainty method in order to measure the roughness of a rough approximation space. This paper discusses the information fusion and uncertainty measure based on rough set theory. First, we propose a new method of information fusion based on the Bayse function, and define a pair of belief function and plausibility function using the fused mass function in an information system. Then we construct entropy for every decision class to measure the roughness of every decision class, and entropy for decision information system to measure the consistence of decision table.
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44

Pfeffer. "AN INTEGRAL IN GEOMETRIC MEASURE THEORY." Real Analysis Exchange 16, no. 1 (1990): 26. http://dx.doi.org/10.2307/44153661.

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45

Kim, M., and A. S. Maida. "Reliability measure theory: a nonmonotonic semantics." IEEE Transactions on Knowledge and Data Engineering 5, no. 1 (1993): 41–51. http://dx.doi.org/10.1109/69.204090.

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46

Fleming, Wendell. "Early developments in geometric measure theory." Indiana University Mathematics Journal 69, no. 1 (2020): 5–36. http://dx.doi.org/10.1512/iumj.2020.69.8229.

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47

Ross, David. "Lifting theorems in nonstandard measure theory." Proceedings of the American Mathematical Society 109, no. 3 (March 1, 1990): 809. http://dx.doi.org/10.1090/s0002-9939-1990-1019753-0.

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48

SORKIN, RAFAEL D. "QUANTUM MECHANICS AS QUANTUM MEASURE THEORY." Modern Physics Letters A 09, no. 33 (October 30, 1994): 3119–27. http://dx.doi.org/10.1142/s021773239400294x.

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The additivity of classical probabilities is only the first in a hierarchy of possible sum rules, each of which implies its successor. The first and most restrictive sum rule of the hierarchy yields measure theory in the Kolmogorov sense, which is appropriate physically for the description of stochastic processes such as Brownian motion. The next weaker sum rule defines a generalized measure theory which includes quantum mechanics as a special case. The fact that quantum probabilities can be expressed "as the squares of quantum amplitudes" is thus derived in a natural manner, and a series of natural generalizations of the quantum formalism is delineated. Conversely, the mathematical sense in which classical physics is a special case of quantum physics is clarified. The present paper presents these relationships in the context of a "realistic" interpretation of quantum mechanics.
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49

Hilger, Stefan. "Matrix Lie theory and measure chains." Journal of Computational and Applied Mathematics 141, no. 1-2 (April 2002): 197–217. http://dx.doi.org/10.1016/s0377-0427(01)00446-0.

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50

Taylor, S. James. "The measure theory of random fractals." Mathematical Proceedings of the Cambridge Philosophical Society 100, no. 3 (November 1986): 383–406. http://dx.doi.org/10.1017/s0305004100066160.

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In 1951 A. S. Besicovitch, who was my research supervisor, suggested that I look at the problem of determining the dimension of the range of a Brownian motion path. This problem had been communicated to him by C. Loewner, but it was a natural question which had already attracted the attention of Paul Lévy. It was a good problem to give to an ignorant Ph.D. student because it forced him to learn the potential theory of Frostman [33] and Riesz[75] as well as the Wiener [98] definition of mathematical Brownian motion. In fact the solution of that first problem in [81] used only ideas which were already twenty-five years old, though at the time they seemed both new and original to me. My purpose in this paper is to try to trace the development of these techniques as they have been exploited by many authors and used in diverse situations since 1953. As we do this in the limited space available it will be impossible to even outline all aspects of the development, so I make no apology for giving a biased account concentrating on those areas of most interest to me. At the same time I will make conjectures and suggest some problems which are natural and accessible in the hope of stimulating further research.
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