Probability and measure

✍ Scribed by Patrick Billingsley

• Publisher: J. Wiley & Sons
• Year: 1995
• Tongue: English
• Leaves: 604
• Edition: 3
• Category: Library

✦ Synopsis

PROBABILITY AND MEASUREThird EditionNow 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.

✦ Table of Contents

Title......Page 1
Copyright Page......Page 2
Preface......Page 3
Contents......Page 5
1. Borel's Normal Number Theorem......Page 12
2. Probability Measures......Page 28
3. Existence and Extension......Page 47
4. Denumerable Probabilities......Page 62
5. Simple Random Variables......Page 78
6. The Law of Large Numbers......Page 96
7. Gambling Systems......Page 103
8. Markov Chains......Page 122
9. Large Deviations and the Law of the Iterated Logarithm......Page 156
10. General Measures......Page 169
11. Outer Measure......Page 176
12. Measures in Euclidean Space......Page 182
13. Measurable Functions and Mappings......Page 193
14. Distribution Functions......Page 198
15. The Integral......Page 210
16. Properties of the Integral......Page 217
17. The Integral with Respect to Lebesgue Measure......Page 232
18. Product Measure and Fubini's Theorem......Page 242
19. The L^p Spaces......Page 252
20. Random Variables and Distributions......Page 265
21. Expected Values......Page 284
22. Sums of Independent Random Variables......Page 293
23. The Poisson Process......Page 308
24. The Ergodic Theorem......Page 321
25. Weak Convergence......Page 338
26. Characteristic Functions......Page 353
27. The Central Limit Theorem......Page 368
28. Infinitely Divisible Distributions......Page 382
29. Limit Theorems in R^k......Page 389
30. The Method of Moments......Page 399
31. Derivatives on the Line......Page 411
32. The Radon-Nikodym Theorem......Page 430
33. Conditional Probability......Page 438
34. Conditional Expectation......Page 456
35. Martingales......Page 469
36. Kolmogorov's Existence Theorem......Page 493
37. Brownian Motion......Page 509
38. Nondenumerable Probabilities......Page 537
APPENDIX......Page 547
NOTES ON THE PROBLEMS......Page 563
BIBLIOGRAPHY......Page 592
LIST OF SYMBOLS......Page 596
INDEX......Page 598