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## Details

Genre/Form: | Electronic books |
---|---|

Additional Physical Format: | Print version: Billingsley, Patrick. Probability and measure. Hoboken, N.J. : Wiley, ©2012 (DLC) 2012382323 (OCoLC)780289503 |

Material Type: | Document, Internet resource |

Document Type: | Internet Resource, Computer File |

All Authors / Contributors: |
Patrick Billingsley |

ISBN: | 9781118341896 1118341899 |

OCLC Number: | 794327535 |

Description: | 1 online resource |

Contents: | Cover; Series Page; Title Page; Copyright; Foreword; Preface; Patrick Billingsley: probability theorist and actor, 1925-2011; Chapter 1: Probability; Section 1 Borel's Normal Number Theorem; Section 2 Probability Measures; Section 3 Existence and Extension; Section 4 Denumerable Probabilities; Section 5 Simple Random Variables; Convergence of Random Variables; Section 6 The Law of Large Numbers; Section 7 Gambling Systems; Section 8 Markov Chains; Section 9 Large Deviations and the Law of the Iterated Logarithm; Chapter 2: Measure; Section 10 General Measures; Section 11 Outer Measure. Section 12 Measures in Euclidean SpaceSection 13 Measurable Functions and Mappings; Section 14 Distribution Functions; Chapter 3: Integration; Section 15 The Integral; Section 16 Properties Of The Integral; Section 17 The Integral With Respect To Lebesgue Measure; Section 18 Product Measure And Fubini'S Theorem; Section 19 The Lp Spaces; Chapter 4: Random Variables and Expected Values; Section 20 Random Variables and Distributions; Section 21 Expected Values; Section 22 Sums of Independent Random Variables; Section 23 The Poisson Process; Section 24 The Ergodic Theorem. Chapter 5: Convergence of DistributionsSection 25 Weak Convergence; Section 26 Characteristic Functions; Section 27 The Central Limit Theorem; Section 28 Infinitely Divisible Distributions; Section 29 Limit Theorems in Rk; Section 30 The Method of Moments; Chapter 6: Derivatives and Conditional Probability; Section 31 Derivatives on the Line; Section 32 The Radon-Nikodym Theorem; Section 33 Conditional Probability; Section 34 Conditional Expectation; Section 35 Martingales; Chapter 7: Stochastic Processes; Section 36 Kolmogorov's Existence Theorem; Section 37 Brownian Motion. Section 38 Nondenumerable ProbabilitiesAppendix; Notes on the Problems; Bibliography; List of Symbols; Index. |

Series Title: | Wiley series in probability and statistics. |

### Abstract:

Praise for the Third Edition"It is, as far as I'm concerned, among the best books in math ever written ... if you are a mathematician and want to have the top reference in probability, this is it." (Amazon.com, January 2006)A complete and comprehensive classic in probability and measure theoryProbability and Measure, Anniversary Edition by Patrick Billingsley celebrates the achievements and advancements that have made this book a classic in its field for the past 35 years. Now re-issued in a new style and format, but with the reliable content that the third edition was revered for, this Anniver.

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