Foundations of Abstract Analysis

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Sprache: Englisch

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Beschreibung

Foundations of Abstract Analysis is the first of a two book series offered as the second (expanded) edition to the previously published text Real Analysis. It is written for a graduate-level course on real analysis and presented in a self-contained way suitable both for classroom use and for self-study.

While this book carries the rigor of advanced modern analysis texts, it elaborates the material in much greater details and therefore fills a gap between introductory level texts (with topics developed in Euclidean spaces) and advanced level texts (exclusively dealing with abstract spaces) making it accessible for a much wider interested audience.

To relieve the reader of the potential overload of new words, definitions, and concepts, the book (in its unique feature) provides lists of new terms at the end of each section, in a chronological order. Difficult to understand abstract notions are preceded by informal discussions and blueprints followed by thorough details and supported by examples and figures. To further reinforce the text, hints and solutions to almost a half of more than 580 problems are provided at the end of the book, still leaving ample exercises for assignments. This volume covers topics in point-set topology and measure and integration.
Prerequisites include advanced calculus, linear algebra, complex variables, and calculus based probability.

Über den Autor

Jewgeni H. Dshalalow is a professor at the Florida Institute of Technology, in Melbourne, Florida, USA.

Zusammenfassung

Systematic presentation with cutting edge classical themes in point-set topology and measure/integration

Fills a gap between basic and advanced texts through rigorous and yet detailed treatment of topics

Includes solutions to hundreds of problems which help reinforce the text

Key analytical formations preceded by blueprints and discussions

Many historical and biographical inserts on subjects and people

Includes supplementary material: [...]

Inhaltsverzeichnis

Set-Theoretic and Algebraic Preliminaries.- Analysis of Metric Spaces.- Elements of Point-Set Topology.-Measurable Spaces and Measurable Functions.- Measures.- Integration in Abstract Spaces.- Solutions to Selected Problems.- Bibliography.-List of Symbols.-Index of Names and Terms.

Details

Erscheinungsjahr:	2016
Fachbereich:	Analysis
Genre:	Mathematik
Rubrik:	Naturwissenschaften & Technik
Medium:	Taschenbuch
Seiten:	764
Inhalt:	xiii 748 S. 8 s/w Illustr. 22 farbige Illustr. 748 p. 30 illus. 22 illus. in color.
ISBN-13:	9781493943883
ISBN-10:	149394388X
Sprache:	Englisch
Ausstattung / Beilage:	Paperback
Einband:	Kartoniert / Broschiert
Autor:	Dshalalow, Jewgeni H.
Auflage:	Softcover reprint of the original 2nd ed. 2013
Hersteller:	Springer US Springer New York
Maße:	235 x 155 x 41 mm
Von/Mit:	Jewgeni H. Dshalalow
Erscheinungsdatum:	23.08.2016
Gewicht:	1,136 kg

preigu-id: 103425594