Integration - Jacques Simon

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Résumé :

Introduction xi
List of Notations and Figures xv

Part 1. Integration 1

Chapter 1. Integration of Continuous Functions 3
1.1. Neumann spaces 3
1.2. Continuous mappings 7
1.3. Cauchy integral of a uniformly continuous function 10
1.4. Some properties of the integral 13
1.5. Dependence of the integral on the domain of integration 16
1.6. Continuity of the integral 19
1.7. Successive integration 21

Chapter 2. Measurable Sets 23
2.1. Why introduce measurable sets? 23
2.2. Some properties of the measure of an open set 25
2.3. Definition of measurable sets and their measure 28
2.4. First properties of the measure 32
2.5. Additivity of the measure 34
2.6. Countable union and countable intersection of measurable sets 37
2.7. Continuity of the measure 40
2.8. Translation invariance and the product measure 44
2.9. Negligible sets 47

Chapter 3. Measures 51
3.1. Space of measuresM(?...

Biographie:
E) 54
3.3. Sequential completeness ofM(?...

Sommaire:
E) 51
3.2. Equicontinuity of bounded subsets ofM(?...