دانلود کتاب Hausdorff measures

فهرست مطالب :

Title page ......Page 1
Date-line ......Page 2
CONTENTS ......Page 3
Preface ......Page 5
2 Measures in abstract spaces ......Page 7
3 Measures in topological spaces ......Page 28
4 Measures in metric spaces ......Page 32
5 Lebesgue measure in $n$-dimensional Euclidean space ......Page 46
6 Metric measures in topological spaces ......Page 49
7 The Souslin operation ......Page 50
1 Definition of Hausdorff measures and equivalent definitions ......Page 56
2 Mappings, special Hausdorff measures, surface areas ......Page 59
3 Existence theorems ......Page 64
4 Comparison theorems ......Page 84
5 Souslin sets ......Page 90
6 The increasing sets lemma and its consequences ......Page 96
7 The existence of comparable net measures and their properties ......Page 107
8 Sets of non-$\\sigma$-finite measure ......Page 129
1 A survey of applications of Hausdorff measures ......Page 134
2 Sets of real numbers defined in terms of their expansions into continued fractions ......Page 141
3 The space of non-decreasing continuous functions defined on the closed unit interval ......Page 153
Bibliography ......Page 175
Index ......Page 183