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Beschreibung
This textbook is designed for a year-long course in real analysis taken by beginning graduate and advanced undergraduate students in mathematics and other areas such as statistics, engineering, and economics. Written by one of the leading scholars in the field, it elegantly explores the core concepts in real analysis and introduces new, accessible methods for both students and instructors. The… first half of the book develops both Lebesgue measure and, with essentially no additional work for the student, general Borel measures for the real line. Notation indicates when a result holds only for Lebesgue measure. Differentiation and absolute continuity are presented using a local maximal function, resulting in an exposition that is both simpler and more general than the traditional approach. The second half deals with general measures and functional analysis, including Hilbert spaces, Fourier series, and the Riesz representation theorem for positive linear functionals on continuous functions with compact support. To correctly discuss weak limits of measures, one needs the notion of a topological space rather than just a metric space, so general topology is introduced in terms of a base of neighborhoods at a point. The development of results then proceeds in parallel with results for metric spaces, where the base is generated by balls centered at a point. The text concludes with appendices on covering theorems for higher dimensions and a short introduction to nonstandard analysis including important applications to probability theory and mathematical economics. Dieses Produkt haben wir gerade leider nicht auf Lager.
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Technische Daten
Erscheinungsdatum
27.05.2018
Sprache
Englisch
EAN
9783319808796
Herausgeber
Springer International Publishing
Sonderedition
Nein
Autor
Peter A. Loeb
Seitenanzahl
274
Auflage
Softcover reprint of the original 1st edition 2016
Einbandart
Taschenbuch
Autorenporträt
Peter Loeb is an emeritus Professor of Mathematics at the University of Illinois in Champaign-Urbana. His research is centered on problems of real analysis and applications of model theory to real analysis.
Schlagwörter
Real analysis, Riemann Integral, Lebesgue measure, Hilbert spaces, Banach Spaces
Thema-Inhalt
PBKB - Reelle Analysis, Real-Variablen
PBKF - Funktionalanalysis und Abwandlungen
PBKL - Integralrechnung und -gleichungen
Höhe
235 mm
Breite
15.5 cm
Hersteller: Springer, Europaplatz 3, Heidelberg, Deutschland, 69115, ProductSafety@springernature.com, Springer Nature Customer Service Center GmbH
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