目录
Preface
Acknowledgments
SECTION
0 Prerequisites
CHAPTER Ⅰ: SETS AND CLASSES
1 Set inclusion
2 Unions and intersections
3 Limits， complements， and differences
4 Rings and algebras
5 Generated rings and -rings
6 Monotone classes
CHAPTER Ⅱ: MEASURES AND OUTER MEASUR. ES
7 Measure on rings
8 Measure on intervals
9 Properties of measures
10 Outer measures
11 Measurable sets
CHAPTER Ⅲ: EXTENSION OF MEASURES
12 Properties of induced measures
13 Extension,completion,and approximation
14 Inner measures
15 Lebesgue measure
16 Non measurable cets
CHAPTER Ⅳ: MEASURABLE FUNCTIONS
17 Measure spaces
18 Measurable functions
19 Combinations of measurable functions
20 Sequences of measurable functions
21 Pointwise convergence
22 Convergence in measure
CHAPTER Ⅴ: INTEGRATION
23 Integrable simple functions
24 Sequences of integrable simple functions
25 Integrable functions
26 Sequences of integrable functions
27 Properties of Integrals
CHAPTER Ⅵ: GENERAL SET FUNCTIONS
28 Signed measures
29 Hahn and Jordan decompostions
30 Absolute continuity
31 The Radon-Nikodym theorem
32 Derivatives of signed measures
CHAPTER Ⅶ: PRODUCT SPACES
CHAPTER Ⅷ: TRANSFORMATIONS AND FUNCTIONS
CHAPTER Ⅸ: PROBABILITY
CHAPTER Ⅹ: LOCALLY COMPACT SPACES
CHAPTER Ⅺ: AHHR MEASURE
CHAPTER Ⅻ: MEASURE AND TOPOLOGY IN GROUPS
……
References
Bibliography
List of frequently used symbols
Index
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内容简介
My main purpose in this book is to present a unified treatment of that part of measure theory which in recent years has shown itself to be most useful for its applications in modern analysis. If I have accomplished my purpose, then the book should be found usable both as a text for students and as a source of reference for the more advanced mathematician.
I have tried to keep to a minimum the amount of new and unusual terminology and notation. In the few places where my nomenclature differs from that in the existing literature of measure theory, I was motivated by an attempt to harmonize with the usage of other parts of mathematics. There are, for instance, sound algebraic reasons for using the terms "lattice" and "ring" for certain classes of sets--reasons which are more cogent than the similarities that caused Hausdorff to use "ring" and "field."
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