Author(s): Robert B. Ash
Publisher: AP
Year: 1972
Language: English
Pages: 297
Cover......Page 1
Title Page......Page 2
Copyright......Page 3
Contents......Page 4
Preface......Page 6
1 Sets......Page 8
2 Real Numbers......Page 9
4 Topology......Page 10
5 Vector Spaces......Page 11
6 Zorn's Lemma......Page 12
1.1 INTRODUCTION......Page 14
1.2 FIELDS, sigma-FIELDS, AND MEASURES......Page 16
1.3 EXTENSION OF MEASURES......Page 26
1.4 LEBESGUE-STIELTJES MEASURES AND DISTRIBUTION FUNCTIONS......Page 35
1.5 MEASURABLE FUNCTIONS AND INTEGRATION......Page 47
1.6 BASIC INTEGRATION THEOREMS......Page 56
1.7 COMPARISON OF LEBESGUE AND RIEMANN INTEGRALS......Page 66
2.1 INTRODUCTION......Page 71
2.2 RADON-NIKODYM THEOREM AND RELATED RESULTS......Page 76
2.3 APPLICATIONS TO REAL ANALYSIS......Page 83
2.4 L?SPACES......Page 93
2.5 CONVERGENCE OF SEQUENCES OF MEASURABLE FUNCTIONS......Page 105
2.6 PRODUCT MEASURES AND FUBINI'S THEOREM......Page 109
2.7 MEASURES ON INFINITE PRODUCT SPACES......Page 121
2.8 REFERENCES......Page 125
3.1 INTRODUCTION......Page 126
3.2 BASIC PROPERTIES OF HILBERT SPACES......Page 129
3.3 LINEAR OPERATORS ON NORMED LINEAR SPACES......Page 140
3.4 BASIC THEOREMS OF FUNCTIONAL ANALYSIS......Page 151
3.5 SOME PROPERTIES OF TOPOLOGICAL VECTOR SPACES......Page 163
3.6 REFERENCES......Page 180
4.1 INTRODUCTION......Page 181
4.2 THE DANIELL INTEGRAL......Page 183
4.3 MEASURES ON TOPOLOGICAL SPACES......Page 191
4.4 MEASURES ON UNCOUNTABLY INFINITE PRODUCT SPACES......Page 202
4.5 WEAK CONVERGENCE OF MEASURES......Page 209
4.6 REFERENCES......Page 213
A1 INTRODUCTION......Page 214
A2 CONVERGENCE......Page 215
A3 PRODUCT AND QUOTIENT TOPOLOGIES......Page 221
A4 SEPARATION PROPERTIES AND OTHER WAYS OF CLASSIFYING TOPOLOGICAL SPACES......Page 224
A5 COMPACTNESS......Page 226
A6 SEMICONTINUOUS FUNCTIONS......Page 233
A7 THE STONE-WEIERSTRASS THEOREM......Page 236
A8 TOPOLOGIES ON FUNCTION SPACES......Page 239
A9 COMPLETE METRIC SPACES AND CATEGORY THEOREMS......Page 243
A10 UNIFORM SPACES......Page 247
BIBLIOGRAPHY......Page 254
Solutions to Problems......Page 256
Subject Index......Page 292
