Real Analysis

Nonfiction, Science & Nature, Mathematics, Mathematical Analysis
Cover of the book Real Analysis by Truman Arthur Botts, Edward James McShane, Dover Publications
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Author: Truman Arthur Botts, Edward James McShane ISBN: 9780486165677
Publisher: Dover Publications Publication: November 7, 2013
Imprint: Dover Publications Language: English
Author: Truman Arthur Botts, Edward James McShane
ISBN: 9780486165677
Publisher: Dover Publications
Publication: November 7, 2013
Imprint: Dover Publications
Language: English

This text offers upper-level undergraduates and graduate students a survey of practical elements of real function theory, general topology, and functional analysis. Beginning with a brief discussion of proof and definition by mathematical induction, it freely uses these notions and techniques. The maximality principle is introduced early but used sparingly; an appendix provides a more thorough treatment. The notion of convergence is stated in basic form and presented initially in a general setting. The Lebesgue-Stieltjes integral is introduced in terms of the ideas of Daniell, measure-theoretic considerations playing only a secondary part. The final chapter, on function spaces and harmonic analysis, is deliberately accelerated. Helpful exercises appear throughout the text. 1959 edition.

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This text offers upper-level undergraduates and graduate students a survey of practical elements of real function theory, general topology, and functional analysis. Beginning with a brief discussion of proof and definition by mathematical induction, it freely uses these notions and techniques. The maximality principle is introduced early but used sparingly; an appendix provides a more thorough treatment. The notion of convergence is stated in basic form and presented initially in a general setting. The Lebesgue-Stieltjes integral is introduced in terms of the ideas of Daniell, measure-theoretic considerations playing only a secondary part. The final chapter, on function spaces and harmonic analysis, is deliberately accelerated. Helpful exercises appear throughout the text. 1959 edition.

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