Hausdorff Measures

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Cambridge University Press, Oct 22, 1998 - Mathematics - 195 pages
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When originally published, this text was the first general account of Hausdorff measures, a subject that has important applications in many fields of mathematics. The first of the three chapters contains an introduction to measure theory, paying particular attention to the study of non-sigma-finite measures. The second chapter develops the most general aspects of the theory of Hausdorff measures, and the final chapter gives a general survey of applications of Hausdorff measures followed by detailed accounts of two special applications. This new edition has a foreword by Kenneth Falconer outlining the developments in measure theory since this book first appeared. This book is ideal for graduate mathematicians with no previous knowledge of the subject, but experts in the field will also want a copy for their shelves.
  

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Contents

MEASURES IN ABSTRACT TOPOLOGICAL AND METRIC SPACES
1
3 Measures in topological spaces
22
4 Measures in metric spaces
26
5 Lebesgue measure in 𝑛dimensional Euclidean space
40
6 Metric measures in topological spaces
43
7 The Souslin operation
44
HAUSDORFF MEASURES
50
2 Mappings special Hausdorff measures surface areas
53
6 The increasing sets lemma and its consequences
90
7 The existence of comparable net measures and their properties
101
8 Sets of non𝝈finite measure
123
APPLICATIONS OF HAUSDORFF MEASURES
128
2 Sets of real numbers defined in terms of their expansions into continued fractions
135
3 The space of nondecreasing continuous functions defined on the closed unit interval
147
BIBLIOGRAPHY
169
APPENDIX A DIMENSION PRINTS
177

3 Existence theorems
58
4 Comparison theorems
78
5 Souslin sets
84

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