a survey of the analogies between topological and measure spaces /
First Statement of Responsibility
John C. Oxtoby
PHYSICAL DESCRIPTION
Specific Material Designation and Extent of Item
viii, 95 pages ;
Dimensions
24 cm
SERIES
Series Title
Graduate texts in mathematics ;
Volume Designation
2
INTERNAL BIBLIOGRAPHIES/INDEXES NOTE
Text of Note
Includes bibliographical references (pages 92-93) and index
CONTENTS NOTE
Text of Note
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