## Overview

This text is a single variable real analysis text, designed for the one-year course at the junior, senior, or beginning graduate level. It provides a rigorous and comprehensive treatment of the theoretical concepts of analysis. The book contains most of the topics covered in a text of this nature, but it also includes many topics not normally encountered in comparable texts. These include the Riemann-Stieltjes integral, the Lebesgue integral, Fourier series, the Weiestrass approximation theorem, and an introduction to normal linear spaces.

**KEY TOPICS:** The Real Number System; Sequence Of Real Numbers; Structure Of Point Sets; Limits And Continuity; Differentiation; The Riemann And Riemann-Stieltjes Integral; Series of Real Numbers; Sequences And Series Of Functions; Orthogonal Functions And Fourier Series; Lebesgue Measure And Integration; Logic and Proofs; Propositions and Connectives

**MARKET:** For all readers interested in real analysis.

## Table of contents

*Each chapter concludes with “Notes”, “Miscellaneous Exercises”, and a “Supplemental Reading”.*)

**1. The Real Number System.**

**2. Sequence Of Real Numbers.**

**3. Structure Of Point Sets.**

**4. Limits And Continuity.**

**5. Differentiation.**

**6. The Riemann And Riemann-Stieltjes Integral.**

**7. Series of Real Numbers.**

**8. Sequences And Series Of Functions.**

**9. Orthogonal Functions And Fourier Series.**

**10. Lebesgue Measure And Integration.**

**Appendix: Logic and Proofs.**

**Propositions and Connectives.**

**Bibliography.**

**Hints and Solutions to Selected Exercises.**

**Notation Index.**

**Index.**

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