Measure and Category A Survey of the Analogies between Topological and Measure Spaces - gebunden oder broschiert

EAN (ISBN-13): 9780387905082
ISBN (ISBN-10): 0387905081
Gebundene Ausgabe
Taschenbuch
Erscheinungsjahr: 2007
Herausgeber: Springer-Verlag New York Inc.
124 Seiten
Gewicht: 0,356 kg
Sprache: eng/Englisch

Buch in der Datenbank seit 2007-05-01T18:21:38+02:00 (Zurich)
Detailseite zuletzt geändert am 2024-04-06T20:49:40+02:00 (Zurich)
ISBN/EAN: 0387905081

ISBN - alternative Schreibweisen:
0-387-90508-1, 978-0-387-90508-2
Alternative Schreibweisen und verwandte Suchbegriffe:
Autor des Buches: oxtoby, john main, lebesgue
Titel des Buches: measure and category, spaces between, the space between, 002, non spaces, graduate text mathematics

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Daten vom Verlag:

Autor/in: John C. Oxtoby
Titel: Graduate Texts in Mathematics; Measure and Category - A Survey of the Analogies between Topological and Measure Spaces
Verlag: Springer; Springer US
108 Seiten
Erscheinungsjahr: 1980-09-29
New York; NY; US
Sprache: Englisch
90,94 € (DE)
93,49 € (AT)
100,50 CHF (CH)
Available
X, 108 p.

BB; Hardcover, Softcover / Mathematik/Analysis; Reelle Analysis, Real-Variablen; Verstehen; Kategorie (Math.); Mass (Math.); algebra; automorphism; homological algebra; measure theory; set; set of first category; topological space; topology; Real Functions; K-Theory; Topology; Algebraische Topologie; Topologie; BC

1. Measure and Category on the Line.- Countable sets, sets of first category, nullsets, the theorems of Cantor, Baire and Borel.- 2. Liouville Numbers.- Algebraic and transcendental numbers, measure and category of the set of Liouville numbers.- 3. Lebesgue Measure in r-Space.- Definitions and principal properties, measurable sets, the Lebesgue density theorem.- 4. The Property of Baire.- Its analogy to measurability, properties of regular open sets.- 5. Non-Measurable Sets.- Vitali sets, Bernstein sets, Ulam’s theorem, inaccessible cardinals, the continuum hypothesis.- 6. The Banach-Mazur Game.- Winning strategies, category and local category, indeterminate games.- 7. Functions of First Class.- Oscillation, the limit of a sequence of continuous functions, Riemann integrability.- 8. The Theorems of Lusin and Egoroff.- Continuity of measurable functions and of functions having the property of Baire, uniform convergence on subsets.- 9. Metric and Topological Spaces.- Definitions, complete and topologically complete spaces, the Baire category theorem.- 10. Examples of Metric Spaces.- Uniform and integral metrics in the space of continuous functions, integrable functions, pseudo-metric spaces, the space of measurable sets.- 11. Nowhere Differentiable Functions.- Banach’s application of the category method.- 12. The Theorem of Alexandroff.- Remetrization of a G? subset, topologically complete subspaces.- 13. Transforming Linear Sets into Nullsets.- The space of automorphisms of an interval, effect of monotone substitution on Riemann integrability, nullsets equivalent to sets of first category.- 14. Fubini’s Theorem.- Measurability and measure of sections of plane measurable sets.- 15. The Kuratowski-Ulam Theorem.- Sections of plane sets having the property of Baire,product sets, reducibility to Fubini’s theorem by means of a product transformation.- 16. The Banach Category Theorem.- Open sets of first category or measure zero, Montgomery’s lemma, the theorems of Marczewski and Sikorski, cardinals of measure zero, decomposition into a nullset and a set of first category.- 17. The Poincaré Recurrence Theorem.- Measure and category of the set of points recurrent under a nondissipative transformation, application to dynamical systems.- 18. Transitive Transformations.- Existence of transitive automorphisms of the square, the category method.- 19. The Sierpinski-Erdös Duality Theorem.- Similarities between the classes of sets of measure zero and of first category, the principle of duality.- 20. Examples of Duality.- Properties of Lusin sets and their duals, sets almost invariant under transformations that preserve nullsets or category.- 21. The Extended Principle of Duality.- A counter example, product measures and product spaces, the zero-one law and its category analogue.- 22. Category Measure Spaces.- Spaces in which measure and category agree, topologies generated by lower densities, the Lebesgue density topology.- Supplementary Notes and Remarks.- References.- Supplementary References.