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- Product code: 14323
- ISBN: 0471007102,
ISBN13: 9780471007104,
608 pages, hardback
Published by John Wiley & Sons, 3rd edition, 1995
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Description of Probability and Measure |
This graduate-level text concentrates on measure theory and modern probability based on measure theory. Its unique feature is the way it intertwines the two subjects: probability problems generate an interest in measure theory and measure theory is then developed and applied to probability. In this new edition, queuing theory is replaced by ergodic theory, modern conditional probability is introduced sooner, and the treatment of Brownian motion is improved. Numerous problems are included in the text.
From the back cover:
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.
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Contents of Probability and Measure |
Ch. 1. Probability
1. Borel's Normal Number Theorem
2. Probability Measures
3. Existence and Extension
4. Denumerable Probabilities
5. Simple Random Variables
6. The Law of Large Numbers
7. Gambling Systems
8. Markov Chains
9. Large Deviations and the Law of the Iterated Logarithm
Ch. 2. Measure
10. General Measures
11. Outer Measure
12. Measures in Euclidean Space
13. Measurable Functions and Mappings
14. Distribution Functions
Ch. 3. Integration
15. The Integral
16. Properties of the Integral
17. The Integral with Respect to Lebesgue Measure
18. Product Measure and Fubini's Theorem
19. The L'superscript p' Spaces
Ch. 4. Random Variables and Expected Values
20. Random Variables and Distributions
21. Expected Values
22. Sums of Independent Random Variables
23. The Poisson Process
24. The Ergodic Theorem
Ch. 5. Convergence of Distributions
25. Weak Convergence
26. Characteristic Functions
27. The Central Limit Theorem
28. Infinitely Divisible Distributions
29. Limit Theorems in R'superscript k'
30. The Method of Moments
Ch. 6. Derivatives and Conditional Probability
31. Derivatives on the Line
32. The Radon-Nikodym Theorem
33. Conditional Probability
34. Conditional Expectation
35. Martingales
Ch. 7. Stochastic Processes
36. Kolmogorov's Existence Theorem
37. Brownian Motion
38. Nondenumerable Probabilities
Appendix
Notes on the Problems
Bibliography
List of Symbols
Index
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