Real Analysis

by Edward James McShane, Truman Arthur Botts

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.

Genres: Mathematics

288 pages, Paperback

First published April 12, 2005

Reviews

[David Cohen · Rating 1 out of 5]

For a topic I don't particularly like, this author didn't have much perspective or strategies to add.

[Hunter · Rating 2 out of 5]

There is only one complete ordered field, and it is real.