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 Juha Heinonen
In these lectures, we concentrate on the theory of Lipschitz functions in Euclidean spaces. From the table of contents: Introduction; Extension; Differentiability; Sobolev spaces; Whitney flat forms; Locally standard Lipschitz structures.
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 Robert Rogers, Eugene Boman - Open SUNY Textbooks
This book covers the major topics typically addressed in an introductory undergraduate course in real analysis in their historical order. The book provides guidance for transforming an intuitive understanding into rigorous mathematical arguments.
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.