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|Additional Physical Format:||Print version:
Probability and measure.
Hoboken, N.J. : Wiley, ©2012
|Material Type:||Document, Internet resource|
|Document Type:||Internet Resource, Computer File|
|All Authors / Contributors:||
|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.|