Introduction to Measure and Integration

S. J. Taylor

doi:10.1017/CBO9780511662478

This paperback, which comprises the first part of Introduction to Measure and Probability by J. F. C. Kingman and S. J. Taylor, gives a self-contained treatment of the theory of finite measures in general spaces at the undergraduate level. It sets the material out in a form which not only provides an introduction for intending specialists in measure theory but also meets the needs of students of probability. The theory of measure and integration is presented for general spaces, with Lebesgue measure and the Lebesgue integral considered as important examples whose special properties are obtained. The introduction to functional analysis which follows covers the material to probability theory and also the basic theory of L2-spaces, important in modern physics. A large number of examples is included; these form an essential part of the development.

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Introduction to Measure and Integration

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Contents

Frontmatter
pp i-ii

Contents
pp iii-iv

Preface
pp v-vi

1 - Theory of sets
pp 1-22

2 - Point set topology
pp 23-50

3 - Set functions
pp 51-73

4 - Construction and properties of measures
pp 74-99

5 - Definitions and properties of the integral
pp 100-133

6 - Related spaces and measures
pp 134-165

7 - The space of measurable functions
pp 166-193

8 - Linear functionals
pp 194-222

9 - Structure of measures in special spaces
pp 223-260

Index of notation
pp 261-262

General Index
pp 263-266

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