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.

Real Analysis and Probability (Cambridge Studies in Advanced Mathematics)

Science & Math

Dudley, R. M.

Mathematics

Cambridge University Press

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.

Real Analysis and Probability (Cambridge Studies in Advanced Mathematics, Series Number 74)

This book shows how, when samples become large, the probability laws of large numbers and related facts are guaranteed to hold over wide domains. The author, an acknowledged expert, gives a thorough treatment of the subject, including several topics not found in any previous book, such as the Fernique-Talagrand majorizing measure theorem for Gaussian processes, an extended treatment of Vapnik-Chervonenkis combinatorics, the Ossiander L2 bracketing central limit theorem, the Giné-Zinn bootstrap central limit theorem in probability, the Bronstein theorem on approximation of convex sets, and the Shor theorem on rates of convergence over lower layers. Other recent results of Talagrand and others are surveyed without proofs in separate sections. Problems are included at the end of each chapter so the book can be used as an advanced text. The book will interest mathematicians with an interest in probability, mathematical statisticians, and computer scientists working in computer learning theory.

Uniform Central Limit Theorems (Cambridge Studies in Advanced Mathematics, Series Number 63)

This book shows how, when samples become large, the probability laws of large numbers and related facts are guaranteed to hold over wide domains. The author, an acknowledged expert, gives a thorough treatment of the subject, including several topics not found in any previous book, such as the Fernique-Talagrand majorizing measure theorem for Gaussian processes, an extended treatment of Vapnik-Chervonenkis combinatorics, the Ossiander L2 bracketing central limit theorem, the Giné-Zinn bootstrap central limit theorem in probability, the Bronstein theorem on approximation of convex sets, and the Shor theorem on rates of convergence over lower layers. Other recent results of Talagrand and others are surveyed without proofs in separate sections. Problems are included at the end of each chapter so the book can be used as an advanced text. The book will interest mathematicians with an interest in probability, mathematical statisticians, and computer scientists working in computer learning theory.

Uniform Central Limit Theorems (Cambridge Studies in Advanced Mathematics, Series Number 142)

This classic work on empirical processes has been considerably expanded and revised from the original edition. When samples become large, the probability laws of large numbers and central limit theorems are guaranteed to hold uniformly over wide domains. The author, an acknowledged expert, gives a thorough treatment of the subject, including the Fernique-Talagrand majorizing measure theorem for Gaussian processes, an extended treatment of Vapnik-Chervonenkis combinatorics, the Ossiander L2 bracketing central limit theorem, the Giné-Zinn bootstrap central limit theorem in probability, the Bronstein theorem on approximation of convex sets, and the Shor theorem on rates of convergence over lower layers. This new edition contains several proved theorems not included in the first edition, including the Bretagnolle-Massart theorem giving constants in the Komlos-Major-Tusnady rate of convergence for the classical empirical process, Massart's form of the Dvoretzky-Kiefer-Wolfowitz inequality with precise constant, Talagrand's generic chaining approach to boundedness of Gaussian processes, a characterization of uniform Glivenko-Cantelli classes of functions, Giné and Zinn's characterization of uniform Donsker classes (i.e., classing Donsker uniformly over all probability measures P), and the Bousquet-Koltchinskii-Panchenko theorem that the convex hull of a uniform Donsker class is uniform Donsker. The book will be an essential reference for mathematicians working in infinite-dimensional central limit theorems, mathematical statisticians, and computer scientists working in computer learning theory. Problems are included at the end of each chapter so the book can also be used as an advanced text.

Real Analysis and Probability

Chapman and Hall/CRC

Concrete Functional Calculus (Springer Monographs in Mathematics)

Concrete Functional Calculus focuses primarily on differentiability of some nonlinear operators on functions or pairs of functions.  This  includes composition of two functions, and the product integral, taking a matrix- or operator-valued coefficient function into a solution of a system of linear differential equations with the given coefficients.  In this book existence and uniqueness of solutions are proved under suitable assumptions for nonlinear integral equations with respect to possibly discontinuous functions having unbounded variation.  Key features and topics: Extensive usage of p-variation of functions, and applications to stochastic processes.This work will serve as a thorough reference on its main topics for researchers and graduate students with a background in real analysis and, for Chapter 12, in probability.

Norvaiša, R.

Springer

This series reports on new developments in mathematical research and teaching - quickly, informally and at a high level. Texts that are out of print but still in demand may also be considered. The timeliness of a manuscript is sometimes more important than its form, which may in such cases be preliminary or tentative. Details of the editorial policy and how to submit can be found at www.springer.com/series/304. We recommend contacting the publisher or the series editors at an early stage of your project. Manuscripts should be prepared according to Springer-Verlag's standard specifications. LaTEX style files may be found at www.springer.com&gt; Authors &gt; Author Guidelines.

Lectures in Modern Analysis and Applications III (Lecture Notes in Mathematics, 170)

See the best price to sell, buy, or rent books by Dudley, R. M.. BookScouter helps to compare book prices from 25+ online bookstores and 30+ buyback vendors with a single search.

Books by Dudley, R. M.

See the best price to sell, buy, or rent books by Dudley, R. M.. BookScouter helps to compare book prices from 25+ online bookstores and 30+ buyback vendors with a single search.

Real Analysis and Probability (Cambridge Studies in Advanced Mathematics)

Real Analysis and Probability (Cambridge Studies in Advanced Mathematics, Series Number 74)

Uniform Central Limit Theorems (Cambridge Studies in Advanced Mathematics, Series Number 63)

Uniform Central Limit Theorems (Cambridge Studies in Advanced Mathematics, Series Number 63)

Uniform Central Limit Theorems (Cambridge Studies in Advanced Mathematics, Series Number 142)

Uniform Central Limit Theorems (Cambridge Studies in Advanced Mathematics, Series Number 142)

Real Analysis and Probability (Cambridge Studies in Advanced Mathematics, Series Number 74)

Real Analysis and Probability

Concrete Functional Calculus (Springer Monographs in Mathematics)

Lectures in Modern Analysis and Applications III (Lecture Notes in Mathematics, 170)