Hausdorff Measures

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.