Theory of Functions of a Real Variable (Dover Books on Mathematics) - Softcover

Natanson, I. P.

Softcover

ISBN 10: 048680643X ISBN 13: 9780486806433

Verlag: Dover Publications Inc., 2016

Inhaltsangabe

Originally published in two volumes, this long out-of-print work by a prominent Soviet mathematician presents a thorough examination of the theory of functions of a real variable. Intended for advanced undergraduates and graduate students of mathematics, the treatment offers a clear account of integration theory and a practical introduction to functional analysis. Prerequisites include a background in the foundations of elementary analysis and some familiarity with the theory of irrational numbers, the theory of limits, continuous functions, Riemann integrals, and infinite series.
Volume I covers infinite and point sets, measurable sets and functions, the Lebesgue integral of a bounded function, square-summable functions, functions of finite variations, the Stieltjes integral, absolutely contiguous functions, and the indefinite Lebesgue integral. Volume II addresses singular integrals, trigonometric series, convex functions, point sets in two-dimensional space, measurable functions of several variables and their integration, set functions and their applications in the theory of integration, transfinite numbers, the Baire classification, certain generalizations of the Lebesgue integral, and some ideas from functional analysis. Many chapters feature challenging exercises.

Über diesen Titel

Über die Autorin bzw. den Autor

Soviet mathematician Isidor Pavlovich Natanson (1906–64) was affiliated with St. Petersburg State University. He also wrote a three-volume treatise, Constructive Function Theory. 

Von der hinteren Coverseite

Originally published in two volumes, this long out-of-print work by a prominent Soviet mathematician presents a thorough examination of the theory of functions of a real variable. Intended for advanced undergraduates and graduate students of mathematics, the treatment offers a clear account of integration theory and a practical introduction to functional analysis. Prerequisites include a background in the foundations of elementary analysis and some familiarity with the theory of irrational numbers, the theory of limits, continuous functions, Riemann integrals, and infinite series.
Volume I covers infinite and point sets, measurable sets and functions, the Lebesgue integral of a bounded function, square-summable functions, functions of finite variations, the Stieltjes integral, absolutely contiguous functions, and the indefinite Lebesgue integral. Volume II addresses singular integrals, trigonometric series, convex functions, point sets in two-dimensional space, measurable functions of several variables and their integration, set functions and their applications in the theory of integration, transfinite numbers, the Baire classification, certain generalizations of the Lebesgue integral, and some ideas from functional analysis. Many chapters feature challenging exercises.
Dover republication of the F. Ungar Publishing Company, New York, 1955 (Volume I) and 1960 (Volume II) editions.
www.doverpublications.com

Details zur Ausgabe

• Verlag: Dover Publications Inc.
• Erscheinungsdatum: 2016
• Sprache: Englisch
• ISBN 10: 048680643X
• ISBN 13: 9780486806433
• Einband: Taschenbuch
• Auflage: 1
• Anzahl der Seiten: 560
• Kontakt zum Hersteller: Nicht verfügbar
• Verantwortliche Person: Soc. Agr. La Raia Ss; http://www.la-raia.it; ; Strada Monterotondo, 79; Novi Ligure; 15067; Italien