Real Analysis and Probability

ISBN-13: 9780521007542 / Angielski / Miękka / 2002 / 566 str.

R. M. Dudley; B. Bollobas; W. Fulton

Opis

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.

Recenzje

'The book serves as a clear, rigorous, and complete introduction to modern probability theory using methods of mathematical analysis, and a description of relations between the two fields … it could be very useful for students interested in learning both topics, it can also serve as complementary reading to standard lectures. Teachers preparing their graduate level courses can use the book as an excellent, rigorously written and complete source.' EMS Newsletter

Spis treści

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.