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＜E-Book＞
Geometric Aspects of Probability Theory and Mathematical Statistics / by V.V. Buldygin, A.B. Kharazishvili
(Mathematics and Its Applications ; 514)

Edition	1st ed. 2000.
Publisher	Dordrecht : Springer Netherlands : Imprint: Springer
Year	2000
Language	English
Size	X, 304 p : online resource
Authors	*Buldygin, V.V author Kharazishvili, A.B author SpringerLink (Online service)
Subjects	LCSH:Probabilities LCSH:Statistics  LCSH:Convex geometry  LCSH:Discrete geometry LCSH:Measure theory LCSH:Functional analysis FREE:Probability Theory FREE:Statistics FREE:Convex and Discrete Geometry FREE:Measure and Integration FREE:Functional Analysis
Notes	1. Convex sets in vector spaces -- 2. Brunn-Minkowski inequality -- 3. Convex polyhedra -- 4. Two classical isoperimetric problems -- 5. Some infinite-dimensional vector spaces -- 6. Probability measures and random elements -- 7. Convergence of random elements -- 8. The structure of supports of Borel measures -- 9. Quasi-invariant probability measures -- 10. Anderson inequality and unimodal distributions -- 11. Oscillation phenomena and extensions of measures -- 12. Comparison principles for Gaussian processes -- 13. Integration of vector-valued functions and optimal estimation of stochastic processes -- Appendix 1: Some properties of convex curves -- Appendix 2: Convex sets and number theory -- Appendix 3: Measurability of cardinals It is well known that contemporary mathematics includes many disci­ plines. Among them the most important are: set theory, algebra, topology, geometry, functional analysis, probability theory, the theory of differential equations and some others. Furthermore, every mathematical discipline consists of several large sections in which specific problems are investigated and the corresponding technique is developed. For example, in general topology we have the following extensive chap­ ters: the theory of compact extensions of topological spaces, the theory of continuous mappings, cardinal-valued characteristics of topological spaces, the theory of set-valued (multi-valued) mappings, etc. Modern algebra is featured by the following domains: linear algebra, group theory, the theory of rings, universal algebras, lattice theory, category theory, and so on. Concerning modern probability theory, we can easily see that the clas­ sification of its domains is much more extensive: measure theory on ab­ stract spaces, Borel and cylindrical measures in infinite-dimensional vector spaces, classical limit theorems, ergodic theory, general stochastic processes, Markov processes, stochastical equations, mathematical statistics, informa­ tion theory and many others HTTP:URL=https://doi.org/10.1007/978-94-017-1687-1

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