**Theory of Functions of a Real Variable**

by Shlomo Sternberg

2005**Number of pages**: 393

**Description**:

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.

Download or read it online for free here:

**Download link**

(1.5MB, PDF)

## Similar books

**Analysis Tools with Applications**

by

**Bruce K. Driver**-

**Springer**

These are lecture notes from Real analysis and PDE: Basic Topological, Metric and Banach Space Notions; Riemann Integral and ODE; Lebesbgue Integration; Hilbert Spaces and Spectral Theory of Compact Operators; Complex Variable Theory; etc.

(

**10798**views)

**Mathematical Analysis I**

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.

(

**11347**views)

**Elementary Real Analysis**

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.

(

**14059**views)

**Real Analysis**

by

**A. M. Bruckner, J. B. Bruckner, B. S. Thomson**-

**Prentice Hall**

This book provides an introductory chapter containing background material as well as a mini-overview of much of the course, making the book accessible to readers with varied backgrounds. It uses a wealth of examples to illustrate important concepts.

(

**13828**views)