Measure and Category: A Survey of the Analogies between Topological and Measure Spaces

John C. Oxtoby (auth.)9780387905082, 0387905081, 3540905081

Table of contents :
Front Matter….Pages I-VIII
Measure and Category on the Line….Pages 1-5
Liouville Numbers….Pages 6-9
Lebesgue Measure in r -Space….Pages 10-18
The Property of Baire….Pages 19-21
Non-Measurable Sets….Pages 22-26
The Banach-Mazur Game….Pages 27-30
Functions of First Class….Pages 31-35
The Theorems of Lusin and Egoroff….Pages 36-38
Metric and Topological Spaces….Pages 39-41
Examples of Metric Spaces….Pages 42-44
Nowhere Differentiable Functions….Pages 45-46
The Theorem of Alexandroff….Pages 47-48
Transforming Linear Sets into Nullsets….Pages 49-51
Fubini’s Theorem….Pages 52-55
The Kuratowski-Ulam Theorem….Pages 56-61
The Banach Category Theorem….Pages 62-64
The Poincaré Recurrence Theorem….Pages 65-69
Transitive Transformations….Pages 70-73
The Sierpinski-Erdös Duality Theorem….Pages 74-77
Examples of Duality….Pages 78-81
The Extended Principle of Duality….Pages 82-85
Category Measure Spaces….Pages 86-91
Back Matter….Pages 92-96