Real Analysis and Probability - 1st Edition - ISBN: 9780120652402, 9781483216188

Real Analysis and Probability

1st Edition

Solutions to Problems

Authors: Robert P. Ash
eBook ISBN: 9781483216188
Imprint: Academic Press
Published Date: 28th March 1972
Page Count: 44
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Real Analysis and Probability: Solutions to Problems presents solutions to problems in real analysis and probability. Topics covered range from measure and integration theory to functional analysis and basic concepts of probability; the interplay between measure theory and topology; conditional probability and expectation; the central limit theorem; and strong laws of large numbers in terms of martingale theory.

Comprised of eight chapters, this volume begins with problems and solutions for the theory of measure and integration, followed by various applications of the basic integration theory. Subsequent chapters deal with functional analysis, paying particular attention to structures that can be defined on vector spaces; the connection between measure theory and topology; basic concepts of probability; and conditional probability and expectation. Strong laws of large numbers are also taken into account, first from the classical viewpoint, and then via martingale theory. The final chapter is devoted to the one-dimensional central limit problem, with emphasis on the fundamental role of Prokhorov's weak compactness theorem.

This book is intended primarily for students taking a graduate course in probability.

Table of Contents

Part I: Solutions to Problems

Chapter 1

Section 1.1.

Section 1.2.

Section 1.3

Section 1.4

Section 1.5

Section 1.6

Section 1.7

Chapter 2

Section 2.1

Section 2.2

Section 2.3

Section 2.4

Section 2.5

Section 2.6

Section 2.7

Chapter 3

Section 3.2

Section 3.3

Section 3.4

Section 3.5

Chapter 4

Section 4.2

Section 4.3

Section 4.4

Section 4.5

Chapter 5

Section 5.8

Section 5.9

Section 5.10

Section 5.11

Chapter 6

Section 6.3

Section 6.5

Section 6.6

Chapter 7

Section 7.1

Section 7.2

Section 7.4

Section 7.5

Section 7.6

Section 7.7

Section 7.8

Chapter 8

Section 8.1

Section 8.2

Section 8.3

Section 8.5


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© Academic Press 1972
Academic Press
eBook ISBN:

About the Author

Robert P. Ash

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