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.
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by Pierre Schapira - Université Paris VI
The notes provide a short presentation of the main concepts of differential calculus. Our point of view is the abstract setting of a real normed space, and when necessary to specialize to the case of a finite dimensional space endowed with a basis.
by Shlomo Sternberg
The topology of metric spaces, Hilbert spaces and compact operators, the Fourier transform, measure theory, the Lebesgue integral, the Daniell integral, Wiener measure, Brownian motion and white noise, Haar measure, Banach algebras, etc.
by N. J. Lennes - John Wiley & Sons
This volume is designed as a reference book for a course dealing with the fundamental theorems of infinitesimal calculus in a rigorous manner. The book may also be used as a basis for a rather short theoretical course on real functions.
by Elias Zakon - The Trillia Group
Topics include metric spaces, convergent sequences, open and closed sets, function limits and continuity, sequences and series of functions, compact sets, power series, Taylor's theorem, differentiation and integration, total variation, and more.