CONTENTS
Foreword v
Introduction ix
I. General vector measure theory 1
1. Elementary properties of vector measures 1
2. Countably additive vector measures 10
3. The Nikodym Boundedness Theorem 14
4. Rosenthal's lemma and the structure of a
vector measure 18
5. The Caratheodory-Hahn-Kluvanek Extension Theorem
and strongly additive vector measures 25
6. Notes and remarks 31
II. Integration 41
1. Measurable functions 41
2. The Bochner integral 44
3. The Pettis integral 52
4. An elementary version of the Bartle integral 56
5. Notes and remarks 57
III. Analytic Radon-Nikodym theorems and operators on Li(jLt) 59
1. The Radon-Nikodym theorem and Riesz representable
operators on Lx(ji) 59
2. Representable operators, weak compactness and
Radon-Nikodym theorems 67
3. Separable dual spaces and the Radon-Nikodym Property 79
4. Notes and remarks 83
IV. Applications of analytic Radon-Nikodym theorems 97
1. The dual of Lp(ju, X) 97
2. Weakly compact subsets of Li(//, X) 101
3. Gel'fand spaces 106
4. Integral operators on Lp(/u) 107
5. The Lewis-Stegall theorem with a dash of Pelczynski 113
vn
Previous Page Next Page