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140122 ||| eng |
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|a 9789401716871
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|a Buldygin, V.V.
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| 245 |
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|a Geometric Aspects of Probability Theory and Mathematical Statistics
|h Elektronische Ressource
|c by V.V. Buldygin, A.B. Kharazishvili
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| 250 |
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|a 1st ed. 2000
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| 260 |
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|a Dordrecht
|b Springer Netherlands
|c 2000, 2000
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| 300 |
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|a X, 304 p
|b online resource
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| 505 |
0 |
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|a 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
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| 653 |
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|a Functional analysis
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| 653 |
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|a Measure theory
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| 653 |
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|a Functional Analysis
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| 653 |
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|a Statistics
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| 653 |
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|a Convex geometry
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| 653 |
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|a Probability Theory
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| 653 |
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|a Convex and Discrete Geometry
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| 653 |
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|a Measure and Integration
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| 653 |
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|a Discrete geometry
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| 653 |
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|a Statistics
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| 653 |
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|a Probabilities
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| 700 |
1 |
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|a Kharazishvili, A.B.
|e [author]
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| 041 |
0 |
7 |
|a eng
|2 ISO 639-2
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| 989 |
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|b SBA
|a Springer Book Archives -2004
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| 490 |
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|a Mathematics and Its Applications
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| 028 |
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|a 10.1007/978-94-017-1687-1
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| 856 |
4 |
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|u https://doi.org/10.1007/978-94-017-1687-1?nosfx=y
|x Verlag
|3 Volltext
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| 082 |
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|a 519.2
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| 520 |
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|a 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
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