The Theory Of Integration
by L. C. Young
Publisher: Cambridge University Press 1927
Number of pages: 69
In writing this book, I have tried above all to simplify the work of the student. On the one hand, practically no knowledge is assumed (merely what concerns existence of real numbers ,and their symbolism); on the other hand, the ideas of Cauchy, Riemann, Darboux, Weierstrass, familiar to the reader who is acquainted with the elementary theory, are used as much as possible.
Home page url
Download or read it online for free here:
by Richard F. Bass - CreateSpace
Nearly every Ph.D. student in mathematics needs to take a preliminary or qualifying examination in real analysis. This book provides the necessary tools to pass such an examination. The author presents the material in as clear a fashion as possible.
by John Franks - arXiv
My intent is to introduce the Lebesgue integral in a quick, and hopefully painless, way and then go on to investigate the standard convergence theorems and a brief introduction to the Hilbert space of L2 functions on the interval.
by Casper Goffman, at al. - American Mathematical Society
This book features the interplay of two main branches of mathematics: topology and real analysis. The text covers Lebesgue measurability, Baire classes of functions, differentiability, the Blumberg theorem, various theorems on Fourier series, etc.
by J. Hunter, B. Nachtergaele - World Scientific Publishing Company
Introduces applied analysis at the graduate level, particularly those parts of analysis useful in graduate applications. Only a background in basic calculus, linear algebra and ordinary differential equations, and functions and sets is required.