Real Analysis and Probability
Real Analysis and Probability
This classic textbook, now reissued, offers a clear exposition of modern probability theory and of the interplay between the properties of metric spaces and probability measures. The new edition has been made even more self-contained than before; it now includes a foundation of the real number system and the Stone-Weierstrass theorem on uniform approximation in algebras of functions. Several other sections have been revised and improved, and the comprehensive historical notes have been further amplified. A number of new exercises have been added, together with hints for solution.
- Classic text by top-name author
- Comprehensive treatment makes it also a useful reference
- Over 400 exercises, many with hints for solutions
Reviews & endorsements
"A marvelous work which will soon become a standard text in the field for both teaching and reference...a complete and pedagogically perfect presentation of both the necessary preparatory material of real analysis and the proofs througout the text. Some of the topics and proofs are rarely found in other textbooks." Proceedings of the Edinburgh Mathematical Society
Product details
October 2002Paperback
9780521007542
566 pages
246 × 156 × 28 mm
0.77kg
400 exercises
Available
Table of Contents
- 1. Foundations: set theory
- 2. General topology
- 3. Measures
- 4. Integration
- 5. Lp spaces: introduction to functional analysis
- 6. Convex sets and duality of normed spaces
- 7. Measure, topology, and differentiation
- 8. Introduction to probability theory
- 9. Convergence of laws and central limit theorems
- 10. Conditional expectations and martingales
- 11. Convergence of laws on separable metric spaces
- 12. Stochastic processes
- 13. Measurability: Borel isomorphism and analytic sets
- Appendixes: A. Axiomatic set theory
- B. Complex numbers, vector spaces, and Taylor's theorem with remainder
- C. The problem of measure
- D. Rearranging sums of nonnegative terms
- E. Pathologies of compact nonmetric spaces
- Indices.
