Theory of Functions of a Real Variable
by Shlomo Sternberg
Number of pages: 393
I have taught the beginning graduate course in real variables and functional analysis three times in the last five years, and this book is the result. The course assumes that the student has seen the basics of real variable theory and point set topology. Contents: 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 and the spectral theorem, Stone’s theorem, scattering theory.
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by Arthur Latham Baker - John Wiley & Sons
The author used only such methods as are familiar to the ordinary student of Calculus, avoiding those methods of discussion dependent upon the properties of double periodicity, and also those depending upon Functions of Complex Variables.
by Elias Zakon - The TrilliaGroup
This book follows the release of the author's Mathematical Analysis I and completes the material on Real Analysis that is the foundation for later courses. The text is appropriate for any second course in real analysis or mathematical analysis.
by Gerald Teschl - Universitaet Wien
This manuscript provides a brief introduction to Real and (linear and nonlinear) Functional Analysis. It covers basic Hilbert and Banach space theory as well as basic measure theory including Lebesgue spaces and the Fourier transform.
by G. H. Hardy - Cambridge University Press
The ideas of Du Bois-Reymond's 'Infinitarcalcul' are of great and growing importance in all branches of the theory of functions. The author brings the Infinitarcalcul up to date, stating explicitly and proving carefully a number of general theorems.