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## Details

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. |

More information: |

### 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 integration and standard convergence theorems. It also discusses discrete time Markov chains, stationary distributions, and limit theorems.
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## Reviews

*Editorial reviews*

Publisher Synopsis

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 advanced undergraduate students in mathematics ... The topics are well selected to meet the needs of students who are interested in graduate studies in areas related to analysis, probability, stochastic processes and statistics ... This makes the book student-friendly. A motivated student can use it by him- or herself to learn the topics well. -Yimin Xiao, Mathematical Reviews, 2010 Read more...

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