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Lebesgue Theory in the Bidual of C(X)
Samuel Kaplan, University of North Carolina, Chapel Hill, NC

Memoirs of the American Mathematical Society
1996; 127 pp; softcover
Volume: 121
ISBN-10: 0-8218-0463-4
ISBN-13: 978-0-8218-0463-6
List Price: US$46
Individual Members: US$27.60
Institutional Members: US$36.80
Order Code: MEMO/121/579
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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.


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

Table of Contents

  • Introduction
  • Preliminaries
  • \(\mathfrak {L}^\infty\)
  • Convergence
  • Some classical theorems
  • The projection of \(C^{\prime\prime}\) onto \(C^{\prime\prime}_a\)
  • Lebesgue theory in \(C^{\prime\prime}_a\)
  • References
  • Index of terminology
  • Index of symbols
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