Probability and Measure
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PROBABILITY AND MEASURE Third Edition Now in its new third edition, Probability and Measure offers advanced students, scientists, and engineers an integrated introduction to measure theory and probability. Retaining the unique approach of the previous editions, this text interweaves material on probability and measure, so that probability problems generate an interest in measure theory and measure theory is then developed and applied to probability. Probability and Measure provides thorough coverage of probability, measure, integration, random variables and expected values, convergence of distributions, derivatives and conditional probability, and stochastic processes. The Third Edition features an improved treatment of Brownian motion and the replacement of queuing theory with ergodic theory. Like the previous editions, this new 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. Booknews A text that offers advanced students, scientists, and engineers an integrated introduction to measure theory and probability. The coverage extends to probability, measure, integration, random variables and expected values, convergence of distributions, derivatives and conditional probability, and stochastic processes. This edition features an improved version of Brownian motion and the replacement of queuing theory with ergodic theory. Annotation c. Book News, Inc., Portland, OR (booknews.com)
Ch. 1Probability11Borel's Normal Number Theorem12Probability Measures173Existence and Extension364Denumerable Probabilities515Simple Random Variables676The Law of Large Numbers857Gambling Systems928Markov Chains1119Large Deviations and the Law of the Iterated Logarithm145Ch. 2Measure15810General Measures15811Outer Measure16512Measures in Euclidean Space17113Measurable Functions and Mappings18214Distribution Functions187Ch. 3Integration19915The Integral19916Properties of the Integral20617The Integral with Respect to Lebesgue Measure22118Product Measure and Fubini's Theorem23119The L[superscript p] Spaces241Ch. 4Random Variables and Expected Values25420Random Variables and Distributions25421Expected Values27322Sums of Independent Random Variables28223The Poisson Process29724The Ergodic Theorem310Ch. 5Convergence of Distributions32725Weak Convergence32726Characteristic Functions34227The Central Limit Theorem35728Infinitely Divisible Distributions37129Limit Theorems in R[superscript k]37830The Method of Moments388Ch. 6Derivatives and Conditional Probability40031Derivatives on the Line40032The Radon-Nikodym Theorem41933Conditional Probability42734Conditional Expectation44535Martingales458Ch. 7Stochastic Processes48236Kolmogorov's Existence Theorem48237Brownian Motion49838Nondenumerable Probabilities526Appendix536Notes on the Problems552Bibliography581List of Symbols585Index587
