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Probability and measure

Author: Patrick Billingsley
Publisher: New York : Wiley, ©1995.
Series: Wiley series in probability and mathematical statistics.
Edition/Format:   Print book : English : 3rd edView all editions and formats
Summary:

The text begins with an introduction to Borel's normal number theorem. Coverage includes key topics in measure, integration, random variables and expected values, convergence of distributions,  Read more...

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Material Type: Internet resource
Document Type: Book, Internet Resource
All Authors / Contributors: Patrick Billingsley
ISBN: 0471007102 9780471007104 0471804789 9780471804789
OCLC Number: 30735805
Notes: "A Wiley-Interscience publication."
Description: xii, 593 pages : illustrations ; 25 cm.
Contents: 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.
Series Title: Wiley series in probability and mathematical statistics.
Responsibility: Patrick Billingsley.
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