Real analysis and probability

R.M. Dudley

566 pages, parution le 25/10/2002 (2^eme édition)

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Résumé

This classic textbook offers a clear exposition of modern probability theory and of the interplay between the properties of metric spaces and probability measures. The first half of the book gives an exposition of real analysis: basic set theory, general topology, measure theory, integration, an introduction to functional analysis in Banach and Hilbert spaces, convex sets and functions and measure on topological spaces.The second half introduces probability based on measure theory, including laws of large numbers, ergodic theorems, the central limit theorem, conditional expectations and martingale's convergence.A chapter on stochastic processes introduces Brownian motion and the Brownian bridge. 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.Contents

Foundations: set theory
General topology
Measures
Integration
Lp spaces: introduction to functional analysis
Convex sets and duality of normed spaces
Measure, topology, and differentiation
Introduction to probability theory
Convergence of laws and central limit theorems
Conditional expectations and martingales
Convergence of laws on separable metric spaces
Stochastic processes
Measurability: Borel isomorphism and analytic sets
Appendixes

Caractéristiques techniques

	PAPIER
Éditeur(s)	Cambridge University Press
Auteur(s)	R.M. Dudley
Parution	25/10/2002
Édition	2^eme édition
Nb. de pages	566
Format	15,3 x 22,6
Couverture	Broché
Poids	776g
Intérieur	Noir et Blanc
EAN13	9780521007542
ISBN13	978-0-521-00754-2