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Cover: 9781461269311 | Measure Theory | J. L. Doob | Taschenbuch | xii | Englisch | 2012
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Measure Theory
Taschenbuch von J. L. Doob
Sprache: Englisch

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Beschreibung
This book was planned originally not as a work to be published, but as an excuse to buy a computer, incidentally to give me a chance to organize my own ideas ~n what measure theory every would-be analyst should learn, and to detail my approach to the subject. When it turned out that Springer-Verlag thought that the point of view in the book had general interest and offered to publish it, I was forced to try to write more clearly and search for errors. The search was productive. Readers will observe the stress on the following points. The application of pseudometric spaces. Pseudo metric, rather than metric spaces, are applied to obviate the artificial replacement of functions by equivalence classes, a replacement that makes the use of "almost everywhere" either improper or artificial. The words "function" and "the set on which a function has values at least E" can be taken literally in this book. Pseudometric space properties are applied in many contexts. For example, outer measures are used to pseudometrize classes of sets and the extension of a finite measure from an algebra to a 0" algebra is thereby reduced to finding the closure of a subset of a pseudo metric space.
This book was planned originally not as a work to be published, but as an excuse to buy a computer, incidentally to give me a chance to organize my own ideas ~n what measure theory every would-be analyst should learn, and to detail my approach to the subject. When it turned out that Springer-Verlag thought that the point of view in the book had general interest and offered to publish it, I was forced to try to write more clearly and search for errors. The search was productive. Readers will observe the stress on the following points. The application of pseudometric spaces. Pseudo metric, rather than metric spaces, are applied to obviate the artificial replacement of functions by equivalence classes, a replacement that makes the use of "almost everywhere" either improper or artificial. The words "function" and "the set on which a function has values at least E" can be taken literally in this book. Pseudometric space properties are applied in many contexts. For example, outer measures are used to pseudometrize classes of sets and the extension of a finite measure from an algebra to a 0" algebra is thereby reduced to finding the closure of a subset of a pseudo metric space.
Inhaltsverzeichnis
0. Conventions and Notation.- I. Operations on Sets.- II. Classes of Subsets of a Space.- III. Set Functions.- IV. Measure Spaces.- V. Measurable Functions.- VI. Integration.- VII. Hilbert Space.- VIII. Convergence of Measure Sequences.- IX. Signed Measures.- X. Measures and Functions of Bounded Variation on R.- XI. Conditional Expectations ; Martingale Theory.- Notation.
Details
Erscheinungsjahr: 2012
Fachbereich: Analysis
Genre: Importe, Mathematik
Rubrik: Naturwissenschaften & Technik
Medium: Taschenbuch
Inhalt: xii
212 S.
ISBN-13: 9781461269311
ISBN-10: 1461269318
Sprache: Englisch
Einband: Kartoniert / Broschiert
Autor: Doob, J. L.
Auflage: Softcover reprint of the original 1st edition 1994
Hersteller: Springer US
Springer New York
Verantwortliche Person für die EU: Springer Verlag GmbH, Tiergartenstr. 17, D-69121 Heidelberg, juergen.hartmann@springer.com
Maße: 235 x 155 x 13 mm
Von/Mit: J. L. Doob
Erscheinungsdatum: 02.10.2012
Gewicht: 0,353 kg
Artikel-ID: 106118762
Inhaltsverzeichnis
0. Conventions and Notation.- I. Operations on Sets.- II. Classes of Subsets of a Space.- III. Set Functions.- IV. Measure Spaces.- V. Measurable Functions.- VI. Integration.- VII. Hilbert Space.- VIII. Convergence of Measure Sequences.- IX. Signed Measures.- X. Measures and Functions of Bounded Variation on R.- XI. Conditional Expectations ; Martingale Theory.- Notation.
Details
Erscheinungsjahr: 2012
Fachbereich: Analysis
Genre: Importe, Mathematik
Rubrik: Naturwissenschaften & Technik
Medium: Taschenbuch
Inhalt: xii
212 S.
ISBN-13: 9781461269311
ISBN-10: 1461269318
Sprache: Englisch
Einband: Kartoniert / Broschiert
Autor: Doob, J. L.
Auflage: Softcover reprint of the original 1st edition 1994
Hersteller: Springer US
Springer New York
Verantwortliche Person für die EU: Springer Verlag GmbH, Tiergartenstr. 17, D-69121 Heidelberg, juergen.hartmann@springer.com
Maße: 235 x 155 x 13 mm
Von/Mit: J. L. Doob
Erscheinungsdatum: 02.10.2012
Gewicht: 0,353 kg
Artikel-ID: 106118762
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