This book is a systematic exposition of the theory of measure and integration. It is intendend for students, and also as a reference work. The body of the text can be read by a student with a firm background in analysis, whereas the supplements treat more advanced topics, and require somewhat more maturity. Although the results given here are the standard ones, the authors have taken a new approach, systematically exploiting the concepts of -ring and -simplicity.
Content Level » Professional/practitioner
Related subjects » Analysis
Author(s): John L. Kelley, T.P. Srinivasan
Series: Graduate Texts in Mathematics 116
Edition: Softcover reprint of the original 1st ed. 1988
Publisher: Springer
Year: 2011
Language: English
Pages: C+X+150+B
Cover
Graduate Texts in Mathematics 116
Measure and Integralm Volume 1
Copyright
© 1988 by Springer-Verlag
ISBN 0-387-96633-1
QA312.K44 1988 515.4'2-dcl9
87-26571
PREFACE
CONTENTS
Chapter 0 PRELIMINARIES
SETS
FUNCTIONS
COUNTABILITY
ORDERINGS AND LATTICES
CONVERGENCE IN R*
UNORDERED SUMMABILI T Y
HAUSDORFF MAXIMAL PRINCIPLE
Chapter 1 PRE-MEASURES
SUPPLEMENT: G INVARIANT CONTENTS
SUPPLEMENT: CARATHEODORY PRE-MEASURES
Chapter 2 PRE-MEASURE TO PRE-INTEGRAL
SUPPLEMENT: PRE-INTEGRALS ON CJX) AND C0(X)
Chapter 3 PRE-INTEGRAL TO INTEGRAL
Chapter 4 INTEGRAL TO MEASURE
SUPPLEMENT: L EBESG UE MEASURE A" FOR R"
SUPPLEMENT: MEASURES ON B(X)
SUPPLEMENT: G INVARIANT MEASURES
Chapter 5 MEASURABILITY AND a-SIMPLICITY
SUPPLEMENT: STANDARD BOREL SPACES
Chapter 6 THE INTEGRAL Iµ ON L1(µ)
SUPPLEMENT: BOREL MEASURES AND POSITIVE FUNCTIONALS
Chapter 7 INTEGRALS* AND PRODUCTS
SUPPLEMENT: BOREL PRODUCT MEASURE
Chapter 8 MEASURES* AND MAPPINGS
SUPPLEMENT: THE IMAGE OF Ap UNDERA SMOOTH MAP
SUPPLEMENT: MAPS OF BOREL MEASURES*; CONVOLUTION
Chapter 9 SIGNED MEASURES AND INDEFINITE INTEGRALS
SUPPLEMENT: DECOMPOSABLE MEASURES
SUPPLEMENT: HAAR MEASURE
Chapter 10 BANACH SPACES
SUPPLEMENT: THE SPACES Co (X)* AND L 1(p)*
SUPPLEMENT: COMPLEX INTEGRAL AND COMPLEX MEASURE
SUPPLEMENT: THE BOCHNER INTEGRAL
SELECTED REFERENCES
ADDITIONAL TITLES
INDEX
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