Theory of Functions of a Real Variable - Hardcover
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.
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.
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About the Author:
Soviet mathematician Isidor Pavlovich Natanson (1906–64) was affiliated with St. Petersburg State University. He also wrote a three-volume treatise, Constructive Function Theory.
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- PublisherFrederick Ungar
- Publication date1955
- ISBN 10 0094551804
- ISBN 13 9780094551800
- BindingHardcover
- Edition number1
- Number of pages277
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Theory of Functions of a Real Variable
Published by
Frederick Ungar
(1955)
ISBN 10: 0094551804
ISBN 13: 9780094551800
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Hardcover
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Book Description Condition: Good. Good condition. No Dust Jacket (Mathematics) A copy that has been read but remains intact. May contain markings such as bookplates, stamps, limited notes and highlighting, or a few light stains. Bundled media such as CDs, DVDs, floppy disks or access codes may not be included. Seller Inventory # E21OS-01734
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