Probability and Measure TheoryProbability and Measure Theory, Second Edition, is a text for a graduatelevel course in probability that includes essential background topics in analysis. It provides extensive coverage of conditional probability and expectation, strong laws of large numbers, martingale theory, the central limit theorem, ergodic theory, and Brownian motion.

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Contents
Fundamentals of Measure and Integration Theory  1 
Further Results in Measure and Integration Theory  60 
Introduction to Functional Analysis  127 
Basic Concepts of Probability  166 
Conditional Probability and Expectation  201 
Strong Laws of Large Numbers and Martingale Theory  235 
The Central Limit Theorem  290 
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Common terms and phrases
afield absolutely continuous arbitrary assume Borel measurable function Borel sets bounded Brownian motion characteristic function complexvalued continuity points converges a.e. converges weakly countably additive crfield defined definition denoted density disjoint sets distribution function dominated convergence theorem entropy ergodic example exists f(co finite measure finitely additive Fubini's theorem function F given h(co hence Hilbert space hypothesis implies increasing sequence independent random variables inequality infinitely divisible large numbers Lebesgue measure LebesgueStieltjes measure Lemma Let F lim sup liminf limit linear operator martingale measurable rectangles measure space measurepreserving transformation nonnegative normed linear space obtain orthonormal pointwise positive integer probability measure probability space Problem Proof properties prove real numbers realvalued result follows rightcontinuous Section set function signed measure simple functions submartingale subspace supermartingale uniformly integrable vector space