Lebesgue theory in the bidual of
About this Title
Publication: Memoirs of the American Mathematical Society
Publication Year 1996: Volume 121, Number 579
ISBNs: 978-0-8218-0463-6 (print); 978-1-4704-0164-1 (online)
MathSciNet review: 1329941
MSC (1991): Primary 46B42; Secondary 28B05, 46Exx, 46F05, 46G99
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
- 2. Convergence
- 3. Some classical theorems
- 4. The projection of onto
- 5. Lebesgue Theory in