# Lebesgue Theory in the Bidual of C(X)

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*Samuel Kaplan*

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.

#### 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