Lebesgue Theory in the Bidual of C(X).

Intro -- Contents -- Introduction -- 1 Preliminaries -- Chapter 1 [omitted][sup(∞)] -- 2 The upper and lower "envelopes" of an element -- 3 The "boundary" of an element -- 4 The "integrable elements -- 5 The negligible elements -- 6 The "μ-integrable elements -- Chapter 2 Convergence -- 7 Almost everywhere order convergence -- 8 Unbounded order convergence -- 9 Almost everywhere unbounded order convergence -- 10 The Dieudonné topology -- 11 Convergence in Measure -- 12 Sequences in [omitted][sup(∞)] -- Chapter 3 Some classical theorems -- 13 Elementary theorems -- 14 The Egorov Theorem -- 15 The Lusin Theorem -- Chapter 4 The Projection of C" onto C"[sub(α)] -- 16 The star elements -- 17 [omitted][sup(∞)] and the star elements -- 18 [omitted][sup(∞)][sub(α)] -- 19 Convergence in C"[sub(α)] -- 20 Back to [omitted][sup(∞)][sub(α)] -- Chapter 5 Lebesgue Theory in C"[sub(α)] -- 21 ∫[sup(*)]fdμ, ∫[sub(*)]fdμ -- 22 ∫fdμ -- 23 The classical theorems -- References -- Index of Terminology -- Index of Symbols.

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Electronic reproduction. Ann Arbor, Michigan : ProQuest Ebook Central, 2024. Available via World Wide Web. Access may be limited to ProQuest Ebook Central affiliated libraries.