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 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 B. S. Thomson, J. B. Bruckner, A. M. Bruckner - Prentice Hall
The book is written in a rigorous, yet reader friendly style with motivational and historical material that emphasizes the big picture and makes proofs seem natural rather than mysterious. Introduces key concepts such as point set theory and other.
by Shanti Narayan - S.Chand And Company
Contents: Dedekind's theory of Real Numbers; Bounds and Limiting Points; Sequences; Real Valued Functions of a Real Variable; The derivative; Riemann Theory of Integration; Uniform Convergence; Improper Integrals; Fourier Series; and more.
by Krzysztof Ciesielski - Heldermann Verlag
This text surveys the recent results that concern real functions whose statements involve the use of set theory. The choice of the topics follows the author's personal interest in the subject. Most of the results are left without the proofs.