Real analysis and probability

REAL ANALYSIS AND PROBABILITY

This much admired textbook, now reissued in paperback, offers a clear expo-

sition 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 func-

tional 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,

of functions. Several other sections have been revised and improved, and

the extensive historical notes have been further amplified. A number of new

exercises, and hints for solution of old and new ones, have been added.

R. M. Dudley is Professor of Mathematics at the Massachusetts Institute of

Technology in Cambridge, Massachusetts.

CAMBRIDGE STUDIES IN ADVANCED MATHEMATICS

Editorial Board:

B. Bollobas, W. Fulton, A. Katok, F. Kirwan, P. Sarnak

Already published

17 W. Dicks & M. Dunwoody Groups acting on graphs

24 H. Kunita Stochastic flows and stochastic differential equations

25 P. Wojtaszczyk Banach spaces for analysts

26 J.E. Gilbert & M.A.M. Murray Clifford algebras and Dirac operators in

harmonic analysis

27 A. Frohlich & M.J. Taylor Algebraic number theory

28 K. Goebel & W.A. Kirk Topics in metric fixed point theory

29 J.F. Humphreys Reflection groups and Coxeter groups

30 D.J. Benson Representations and cohomology I

31 D.J. Benson Representations and cohomology II

32 C. Allday & V. Puppe Cohomological methods in transformation groups

40 V. Snaith Explicit Brauer induction

41 G. Laumon Cohomology of Drinfeld modular varieties I

42 E.B. Davies Spectral theory and differential operators

43 J. Diestel, H. Jarchow, & A. Tonge Absolutely summing operators

44 P. Mattila Geometry of sets and measures in Euclidean spaces

45 R. Pinsky Positive harmonic functions and diffusion

46 G. Tenenbaum Introduction to analytic and probabilistic number theory

47 C. Peskine An algebraic introduction to complex projective geometry

48 Y. Meyer & R. Coifman Wavelets

49 R. Stanley Enumerative combinatorics I

56 G. Laumon Cohomology of Drinfeld modular varieties II

57 D.M. Clark & B.A. Davey Natural dualities for the working algebraist

58 J. McCleary A user’s guide to spectral sequences II

59 P. Taylor Practical foundations of mathematics

60 M.P. Brodmann & R.Y. Sharp Local cohomology

61 J.D. Dixon et al. Analytic pro-P groups

62 R. Stanley Enumerative combinatorics II

63 R.M. Dudley Uniform central limit theorems

64 J. Jost & X. Li-Jost Calculus of variations

65 A.J. Berrick & M.E. Keating An introduction to rings and modules

72 F. Borceaux & G. Janelidze Galois theories

73 B. Bollobas Random graphs

REAL ANALYSIS AND

PROBABILITY

R. M. DUDLEY