Real Analysis And Probability

R EAL ANALYSIS AND PROBABILITY

This much admired textbook, now reissued in paperback, 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 functionalanalysis 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 convergence. A chapter on stochastic processes introduces Brownian motion and the
Brownian bridge.
The new editionhas been made even more self-contained than before;
it now includes early in the book 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 extensive historical notes have been further amplified. A number of new
exercises, and hints for solution of old and newones, 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
18 L.J. Corwin & F.P. Greenleaf Representations of nilpotent Lie groupsand their
applications
19 R. Fritsch & R. Piccinini Cellular structures in topology
20 H. Klingen Introductory lectures on Siegel modular forms
21 P. Koosis The logarithmic integral II
22 M.J. Collins Representations and characters of finite groups
24 H. Kunita Stochastic flows and stochastic differential equations
25 P. Wojtaszczyk Banach spaces for analysts
26 J.E. Gilbert & M.A.M. MurrayClifford 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 groups33 C. Soule et al. Lectures on Arakelov geometry
34 A. Ambrosetti & G. Prodi A primer of nonlinear analysis
35 J. Palis & F. Takens Hyperbolicity, stability and chaos at homoclinic bifurcations
37 Y. Meyer Wavelets and operators 1
38 C. Weibel An introduction to homological algebra
39 W. Bruns & J. Herzog Cohen-Macaulay rings
40 V. Snaith Explicit Brauer induction
41 G. Laumon Cohomologyof 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 tocomplex projective geometry
48 Y. Meyer & R. Coifman Wavelets
49 R. Stanley Enumerative combinatorics I
50 I. Porteous Clifford algebras and the classical groups
51 M. Audin Spinning tops
52 V. Jurdjevic Geometric control theory
53 H. Volklein Groups as Galois groups
54 J. Le Potier Lectures on vector bundles
55 D. Bump Automorphic forms and representations
56 G. Laumon Cohomology ofDrinfeld 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...