**Memoirs of the American Mathematical Society**

1996;
127 pp;
Softcover

MSC: Primary 46; 28;

Print ISBN: 978-0-8218-0463-6

Product Code: MEMO/121/579

List Price: $46.00

Individual Member Price: $27.60

**Electronic ISBN: 978-1-4704-0164-1
Product Code: MEMO/121/579.E**

List Price: $46.00

Individual Member Price: $27.60

# Lebesgue Theory in the Bidual of C(X)

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*Samuel Kaplan*

This book, based on the author's monograph, “The
Bidual of C(X) I”, throws new light on the subject of
Lebesgue integration and contributes to clarification of the structure
of the bidual of C(X).

Kaplan generalizes to the bidual the theory of Lebesgue integration,
with respect to Radon measures on X, of bounded functions (X is assumed
to be compact). The bidual of C(X) contains this space of bounded
functions, but is much more “spacious”, so the body of
results can be expected to be richer. Finally, the author shows that by
projection onto the space of bounded functions, the standard theory is
obtained.

#### Readership

Graduate students and research mathematicians interested in functional analysis and measure and integrations.

#### Table of Contents

# Table of Contents

## Lebesgue Theory in the Bidual of C(X)

- Contents v6 free
- Introduction 110 free
- §1 Preliminaries 312 free
- Chapter 1 [omitted][sup(∞)] 817
- Chapter 2 Convergence 3140
- Chapter 3 Some classical theorems 6271
- Chapter 4 The Projection of C" onto C"[sub(α)] 7483
- Chapter 5 Lebesgue Theory in C"[sub(α)] 108117
- References 124133
- Index of Terminology 125134 free
- Index of Symbols 126135 free