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Hausdorff Measures: Cambridge Mathematical Library

Autor C. A. Rogers Cuvânt înainte de Kenneth Falconer
en Limba Engleză Paperback – 22 oct 1998
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 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.
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Specificații

ISBN-13: 9780521624916
ISBN-10: 0521624916
Pagini: 228
Ilustrații: Illustrations
Dimensiuni: 151 x 228 x 14 mm
Greutate: 0.34 kg
Ediția:Revizuită
Editura: Cambridge University Press
Colecția Cambridge University Press
Seria Cambridge Mathematical Library

Locul publicării:Cambridge, United Kingdom

Cuprins

Foreword Kenneth Falconer; Preface; Part I. Measures in Abstract, Topological and Metric Spaces: 1. Introduction; 2. Measures in abstract spaces; 3. Measures in topological spaces; 4. Measures in metric spaces; 5. Lebesgue measure in n-dimensional Euclidean space; 6. Metric measures in topological spaces; 7. The Souslin operation; Part II. Hausdorff Measures: 8. Definition of Hausdorff measures and equivalent definitions; 9. Mappings, special Hausdorff measures, surface areas; 10. Existence theorems; 11. Comparison theorems; 12. Souslin sets; 13. The increasing sets lemma and its consequences; 14. The existence of comparable net measures and their properties; 15. Sets of non-σ-finite measure; Part III. Applications of Hausdorff Measures: 16. A survey of applications of Hausdorff measures; 17. Sets of real numbers defined in terms of their expansions into continued fractions; 18. The space of non-decreasing continuous functions defined on the closed unit interval; Bibliography; Appendix; Index.

Recenzii

'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

Descriere

Classic book on measure theory with a foreword by the best name in the field.