Memoirs of the American Mathematical Society 1996; 127 pp; softcover Volume: 121 ISBN10: 0821804634 ISBN13: 9780821804636 List Price: US$43 Individual Members: US$25.80 Institutional Members: US$34.40 Order Code: MEMO/121/579
 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  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
