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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:

* The book is written by a first-class, world-renown authority in probability and measure theory at a leading U.S. institution of higher education * The book has been class-tested at over 200 universities around the globe * Theory is first-and-foremost.
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Publisher Synopsis

Like the previous editions, this Anniversary edition will be well received by students of mathematics, statistics, economics, and a wide variety of disciplines that require a solid understanding of probability theory. (Int. J. Microstructure and Materials Properties, 1 February 2013) Read more...

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