Hausdorff Measures

ISBN-13: 9780521624916 / Angielski / Miękka / 1998 / 228 str.

C. A. Rogers; K. J. Falconer; Kenneth Falconer

Opis

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.

Recenzje

'… well-known and beautiful book … written with notable clarity and precision …' European Mathematical Society

Spis treści

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.