Book contents
- Frontmatter
- Dedication
- Contents
- Preface
- Prologue: Regular Variation
- 1 Preliminaries
- 2 Baire Category and Related Results
- 3 Borel Sets, Analytic Sets and Beyond: Δ21
- 4 Infinite Combinatorics in Rn: Shift-Compactness
- 5 Kingman Combinatorics and Shift-Compactness
- 6 Groups and Norms: BirkhoffKakutani Theorem
- 7 Density Topology
- 8 Other Fine Topologies
- 9 CategoryMeasure Duality
- 10 Category Embedding Theorem and Infinite Combinatorics
- 11 Effros’ Theorem and the Cornerstone Theorems of Functional Analysis
- 12 Continuity and Coincidence Theorems
- 13 * Non-separable Variants
- 14 Contrasts between Category and Measure
- 15 Interior-Point Theorems: Steinhaus–Weil Theory
- 16 Axiomatics of Set Theory
- Epilogue: Topological Regular Variation
- References
- Index
14 - Contrasts between Category and Measure
Published online by Cambridge University Press: 14 January 2025
Book contents
- Frontmatter
- Dedication
- Contents
- Preface
- Prologue: Regular Variation
- 1 Preliminaries
- 2 Baire Category and Related Results
- 3 Borel Sets, Analytic Sets and Beyond: Δ21
- 4 Infinite Combinatorics in Rn: Shift-Compactness
- 5 Kingman Combinatorics and Shift-Compactness
- 6 Groups and Norms: BirkhoffKakutani Theorem
- 7 Density Topology
- 8 Other Fine Topologies
- 9 CategoryMeasure Duality
- 10 Category Embedding Theorem and Infinite Combinatorics
- 11 Effros’ Theorem and the Cornerstone Theorems of Functional Analysis
- 12 Continuity and Coincidence Theorems
- 13 * Non-separable Variants
- 14 Contrasts between Category and Measure
- 15 Interior-Point Theorems: Steinhaus–Weil Theory
- 16 Axiomatics of Set Theory
- Epilogue: Topological Regular Variation
- References
- Index
Summary
As a counterpart to Chapter 9 on category–measure duality, we focus here on a variety of situations in which duality fails. We cover a range of topics: Liouville numbers, Banach–Tarski (‘paradoxical’) decompositions, restriction and continuity, random series, normal numbers, topological and Hausdorff dimension, random Dirichlet series, filters, genericity, the Fubini and Kuratowski–Ulam theorems. We give an account of modern results on forcing, deferring technicalities to Chapter 16.
Keywords
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- Chapter
- Information
- Category and MeasureInfinite Combinatorics, Topology and Groups, pp. 222 - 234Publisher: Cambridge University PressPrint publication year: 2025