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 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 Robert B. Ash - Institute of Electrical & Electronics Engineering
A text for a first course in real variables for students of engineering, physics, and economics, who need to know real analysis in order to cope with the professional literature. The subject matter is fundamental for more advanced mathematical work.
by G.H. Hardy, Marcel Riesz - Cambridge University Press
This classic work explains the theory and formulas behind Dirichlet's series and offers the first systematic account of Riesz's theory of the summation of series by typical means. Its authors rank among the most distinguished mathematicians ...
by Bruce K. Driver - University of California, San Diego
Contents: Natural, integer, and rational Numbers; Fields; Real Numbers; Complex Numbers; Set Operations, Functions, and Counting; Metric Spaces; Series and Sums in Banach Spaces; Topological Considerations; Differential Calculus in One Real Variable.