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Hausdorff Measures : Cambridge Mathematical Library - C. A. Rogers

Hausdorff Measures

Cambridge Mathematical Library

By: C. A. Rogers, Kenneth Falconer (Foreword by)

Paperback Published: 21st December 1998
ISBN: 9780521624916
Number Of Pages: 228

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When it was first published this was the first general account of Hausdorff measures, a subject that has important applications in many fields of mathematics. There are three chapters: the first contains an introduction to measure theory, paying particular attention to the study of non-s-finite measures. The second develops the most general aspects of the theory of Hausdorff measures, and the third 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. Based on lectures given by the author at University College London, 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.

'It is indispensable for anyone wishing to introduce himself in the field of fractal geometry, and also to the researchers in this field.' E. Petrisor, Zentralblatt MATH '... will appeal to experts in the field and can be used as an introduction, with a steep learning curve, for graduate students.' Steve Abbott, The Mathematical Gazette '... well-known and beautiful book ... written with notable clarity and precision ...' European Mathematical Society

Foreword Kenneth Falconer
Preface
Measures in Abstract, Topological and Metric Spaces
Introduction
Measures in abstract spaces
Measures in topological spaces
Measures in metric spaces
Lebesgue measure in n-dimensional Euclidean space
Metric measures in topological spaces
The Souslin operation
Hausdorff Measures
Definition of Hausdorff measures and equivalent definitions
Mappings, special Hausdorff measures, surface areas
Existence theorems
Comparison theorems
Souslin sets
The increasing sets lemma and its consequences
The existence of comparable net measures and their properties
Sets of non-s-finite measure
Applications of Hausdorff Measures
A survey of applications of Hausdorff measures
Sets of real numbers defined in terms of their expansions into continued fractions
The space of non-decreasing continuous functions defined on the closed unit interval
Bibliography
Appendix
Index
Table of Contents provided by Publisher. All Rights Reserved.

ISBN: 9780521624916
ISBN-10: 0521624916
Series: Cambridge Mathematical Library
Audience: Professional
Format: Paperback
Language: English
Number Of Pages: 228
Published: 21st December 1998
Publisher: CAMBRIDGE UNIV PR
Country of Publication: GB
Dimensions (cm): 22.86 x 15.24  x 1.32
Weight (kg): 0.34
Edition Number: 2
Edition Type: Revised