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Geometric Aspects of Probability Theory and Mathematical Statistics

Geometric Aspects of Probability Theory and Mathematical Statistics

Paperback

Series: Mathematics and Its Applications, Book 514

General MathematicsProbability & Statistics

ISBN10: 9048155053
ISBN13: 9789048155057
Publisher: Springer Nature
Published: Dec 9 2010
Pages: 304
Weight: 0.98
Height: 0.66 Width: 6.14 Depth: 9.21
Language: English
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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