Probability and Measure Theory

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Academic Press, 2000 - Mathematics - 516 pages
5 Reviews
Probability and Measure Theory, Second Edition, is a text for a graduate-level 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.


* Clear, readable style
* Solutions to many problems presented in text
* Solutions manual for instructors
* Material new to the second edition on ergodic theory, Brownian motion, and convergence theorems used in statistics
* No knowledge of general topology required, just basic analysis and metric spaces
* Efficient organization
  

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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
Ergodic Theory
345
Brownian Motion and Stochastic Integrals
399
Appendi ices
438
Bibliography
454
Index
512
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About the author (2000)

Robert B. Ash as written about, taught, or studied virtually every area of mathematics. His books include Information Theory, Topics in Stochastic Processes, The Calculus Tutoring Book, Introduction to Discrete Mathematics, and A Primer of Mathematics.

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