Measure and category: a survey of the analogies between topological and measure spaces/
John C. Oxtoby
- 2nd. ed.
- New York: Springer, 1971.
- ix, 106 p. ; 24 cm.
- (Graduate texts in mathematics), 2 .
Measure and category on the line -- Liouville numbers -- Lebesgue measure in r-space -- The property of Baire -- Non-measurable sets -- The Banach-Mazur game -- Functions of first class -- The theorems of Lusin and Egoroff -- Metric and topological spaces -- Examples of metric spaces -- Nowhere differentiable functions -- The theorem of Alexandroff -- Transforming linear sets into nullsets -- Fubini's theorem -- The Kuratowski-Ulam theorem -- The Banach category theorem -- The Poincaré recurrence theorem -- Transitive transformations -- The Sierpinski-Erdös duality theorem -- Examples of duality -- The extended principle of duality -- Category measure spaces.
9780387905082
Measure theory Spaces of measures Topological spaces Topology