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Measure & probability

Author: Siva Athreya; V S Sunder
Publisher: Hyderabad, India : Universities Press ; Boca Raton, FL : [distributor], CRC Press, 2008.
Edition/Format:   Book : EnglishView all editions and formats
Database:WorldCat
Summary:
"This book has been designed primarily for students at the masters and doctoral levels. It covers the fundamentals of measure theory and probability theory. It begins with the construction of Lebesgue measure via Caratheodory's outer measure approach and goes on to discuss integration and standard convergence theorems (monotone and dominated, as well as Fatou's lemma). An entire chapter is devoted to complex  Read more...
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Genre/Form: Textbooks
Document Type: Book
All Authors / Contributors: Siva Athreya; V S Sunder
ISBN: 9788173716133 8173716137 9781439801260 1439801266
OCLC Number: 255900417
Target Audience: Students at masters and doctoral levels.
Description: x, 221 pages ; 25 cm
Contents: Probabilities and Measures Introduction sigma-algebras as events Algebras, monotone classes, etc. Preliminaries on measures Outer measures and Caratheodory extension Lebesgue measure Regularity Bernoulli trials Integration Measurable functions Integration a.e. considerations Random Variables Distribution and expectation Independent events and tail sigma-algebra Some distributions Conditional expectation Probability Measures on Product Spaces Product measures Joint distribution and independence Probability measures on infinite product spaces Kolmogorov consistency theorem Characteristics and Convergences Characteristic functions Modes of convergence Central limit theorem Law of large numbers Markov Chains Discrete time MC Examples Classification of states Strong Markov property Stationary distribution Limit theorems Some Analysis Complex measures Lp spaces Radon-Nikodym theorem Change of variables Differentiation The Riesz representation theorem Appendix Metric spaces Topological spaces Compactness The Stone-Weierstrass theorem Tables References Index
Other Titles: Measure and probability
Responsibility: S.R. Athreya, V.S. Sunder.
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Abstract:

Covers the fundamentals of measure theory and probability theory. This title begins with the construction of Lebesgue measure via Caratheodory's outer measure approach and goes on to discuss  Read more...

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This textbook is suitable for a one-semester course on measure theory and probability for beginning graduate students in mathematics, probability and statistics. It can also be used as a textbook for Read more...

 
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schema:reviewBody""This book has been designed primarily for students at the masters and doctoral levels. It covers the fundamentals of measure theory and probability theory. It begins with the construction of Lebesgue measure via Caratheodory's outer measure approach and goes on to discuss integration and standard convergence theorems (monotone and dominated, as well as Fatou's lemma). An entire chapter is devoted to complex measures, L P spaces, Radon-Nikodym theorem and the Riesz representation theorem. The elements of probability theory (random variables, distributions, independence, product measures spaces) as also the law of large numbers and central limit theorem are presented. Discrete time Markov chains, stationary distributions and limit theorems are then discussed." "Among the highlights are alternative proofs of Riesz representation theorem and the law of large numbers. Finally, the appendix treats many basic topics such as metric spaces, topological spaces and the Stone-Weierstrass theorem."--Jacket."
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