R. M. Dudley (Massachusetts Institute of Technology)

Real Analysis and Probability

Herausgeber: Bollobas, Bela; Fulton, W.

• Broschiertes Buch

Produktbeschreibung

This classic graduate textbook offers a clear exposition of modern probability theory and of the interplay between the properties of metric spaces and probability measures. The comprehensive historical notes have been further amplified for this edition, and a number of new exercises have been added, together with hints for solution.

Produktdetails

• Cambridge Studies in Advanced Mathematics
• Verlag: Cambridge University Press
• 2 Revised edition
• Seitenzahl: 566
• Erscheinungstermin: 17. Januar 2011
• Englisch
• Abmessung: 229mm x 152mm x 34mm
• Gewicht: 836g
• ISBN-13: 9780521007542
• ISBN-10: 0521007542
• Artikelnr.: 21819148

Inhaltsangabe

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.