Measure and Category: A Survey of the Analogies between Topological and Measure Spaces
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
New York, NY
Springer New York
1980
|
| Ausgabe: | Second Edition |
| Schriftenreihe: | Graduate Texts in Mathematics
2 |
| Schlagworte: | |
| Online-Zugang: | Volltext |
| Beschreibung: | In this edition, a set of Supplementary Notes and Remarks has been added at the end, grouped according to chapter. Some of these call attention to subsequent developments, others add further explanation or additional remarks. Most of the remarks are accompanied by a briefly indicated proof, which is sometimes different from the one given in the reference cited. The list of references has been expanded to include many recent contributions, but it is still not intended to be exhaustive. John C. Oxtoby Bryn Mawr, April 1980 Preface to the First Edition This book has two main themes: the Baire category theorem as a method for proving existence, and the "duality" between measure and category. The category method is illustrated by a variety of typical applications, and the analogy between measure and category is explored in all of its ramifications. To this end, the elements of metric topology are reviewed and the principal properties of Lebesgue measure are derived. It turns out that Lebesgue integration is not essential for present purposes-the Riemann integral is sufficient. Concepts of general measure theory and topology are introduced, but not just for the sake of generality. Needless to say, the term "category" refers always to Baire category; it has nothing to do with the term as it is used in homological algebra |
| Beschreibung: | 1 Online-Ressource (X, 108 p) |
| ISBN: | 9781468493399 9781468493412 |
| ISSN: | 0072-5285 |
| DOI: | 10.1007/978-1-4684-9339-9 |
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Datensatz im Suchindex
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| dewey-ones | 515 - Analysis |
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| discipline | Mathematik |
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| spelling | Oxtoby, John C. Verfasser aut Measure and Category A Survey of the Analogies between Topological and Measure Spaces by John C. Oxtoby Second Edition New York, NY Springer New York 1980 1 Online-Ressource (X, 108 p) txt rdacontent c rdamedia cr rdacarrier Graduate Texts in Mathematics 2 0072-5285 In this edition, a set of Supplementary Notes and Remarks has been added at the end, grouped according to chapter. Some of these call attention to subsequent developments, others add further explanation or additional remarks. Most of the remarks are accompanied by a briefly indicated proof, which is sometimes different from the one given in the reference cited. The list of references has been expanded to include many recent contributions, but it is still not intended to be exhaustive. John C. Oxtoby Bryn Mawr, April 1980 Preface to the First Edition This book has two main themes: the Baire category theorem as a method for proving existence, and the "duality" between measure and category. The category method is illustrated by a variety of typical applications, and the analogy between measure and category is explored in all of its ramifications. To this end, the elements of metric topology are reviewed and the principal properties of Lebesgue measure are derived. It turns out that Lebesgue integration is not essential for present purposes-the Riemann integral is sufficient. Concepts of general measure theory and topology are introduced, but not just for the sake of generality. Needless to say, the term "category" refers always to Baire category; it has nothing to do with the term as it is used in homological algebra Mathematics K-theory Topology Real Functions K-Theory Mathematik Baire-Kategoriesatz (DE-588)4143919-3 gnd rswk-swf Topologie (DE-588)4060425-1 gnd rswk-swf Topologischer Raum (DE-588)4137586-5 gnd rswk-swf Mathematik (DE-588)4037944-9 gnd rswk-swf Maßraum (DE-588)4169057-6 gnd rswk-swf Maßtheorie (DE-588)4074626-4 gnd rswk-swf Kategorie Mathematik (DE-588)4129930-9 gnd rswk-swf Maßtheorie (DE-588)4074626-4 s Topologischer Raum (DE-588)4137586-5 s Kategorie Mathematik (DE-588)4129930-9 s 1\p DE-604 Topologie (DE-588)4060425-1 s 2\p DE-604 Maßraum (DE-588)4169057-6 s 3\p DE-604 Baire-Kategoriesatz (DE-588)4143919-3 s 4\p DE-604 Mathematik (DE-588)4037944-9 s 5\p DE-604 https://doi.org/10.1007/978-1-4684-9339-9 Verlag Volltext 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk 2\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk 3\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk 4\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk 5\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Oxtoby, John C. Measure and Category A Survey of the Analogies between Topological and Measure Spaces Mathematics K-theory Topology Real Functions K-Theory Mathematik Baire-Kategoriesatz (DE-588)4143919-3 gnd Topologie (DE-588)4060425-1 gnd Topologischer Raum (DE-588)4137586-5 gnd Mathematik (DE-588)4037944-9 gnd Maßraum (DE-588)4169057-6 gnd Maßtheorie (DE-588)4074626-4 gnd Kategorie Mathematik (DE-588)4129930-9 gnd |
| subject_GND | (DE-588)4143919-3 (DE-588)4060425-1 (DE-588)4137586-5 (DE-588)4037944-9 (DE-588)4169057-6 (DE-588)4074626-4 (DE-588)4129930-9 |
| title | Measure and Category A Survey of the Analogies between Topological and Measure Spaces |
| title_auth | Measure and Category A Survey of the Analogies between Topological and Measure Spaces |
| title_exact_search | Measure and Category A Survey of the Analogies between Topological and Measure Spaces |
| title_full | Measure and Category A Survey of the Analogies between Topological and Measure Spaces by John C. Oxtoby |
| title_fullStr | Measure and Category A Survey of the Analogies between Topological and Measure Spaces by John C. Oxtoby |
| title_full_unstemmed | Measure and Category A Survey of the Analogies between Topological and Measure Spaces by John C. Oxtoby |
| title_short | Measure and Category |
| title_sort | measure and category a survey of the analogies between topological and measure spaces |
| title_sub | A Survey of the Analogies between Topological and Measure Spaces |
| topic | Mathematics K-theory Topology Real Functions K-Theory Mathematik Baire-Kategoriesatz (DE-588)4143919-3 gnd Topologie (DE-588)4060425-1 gnd Topologischer Raum (DE-588)4137586-5 gnd Mathematik (DE-588)4037944-9 gnd Maßraum (DE-588)4169057-6 gnd Maßtheorie (DE-588)4074626-4 gnd Kategorie Mathematik (DE-588)4129930-9 gnd |
| topic_facet | Mathematics K-theory Topology Real Functions K-Theory Mathematik Baire-Kategoriesatz Topologie Topologischer Raum Maßraum Maßtheorie Kategorie Mathematik |
| url | https://doi.org/10.1007/978-1-4684-9339-9 |
| work_keys_str_mv | AT oxtobyjohnc measureandcategoryasurveyoftheanalogiesbetweentopologicalandmeasurespaces |