Modern Real Analysis

• Main Author: Ziemer, William P. (Author)
• Corporate Author: SpringerLink (Online service)
• Format: Electronic eBook
• Language: English
• Published: Cham : Springer International Publishing : Imprint: Springer, 2017.
• Edition: 2nd ed. 2017.
• Series: Graduate Texts in Mathematics, 278
• Subjects: Mathematics.; Functional analysis.; Measure theory.; Functions of real variables.; Real Functions.; Functional Analysis.; Measure and Integration.

This first year graduate text is a comprehensive resource in real analysis based on a modern treatment of measure and integration. Presented in a definitive and self-contained manner, it features a natural progression of concepts from simple to difficult. Several innovative topics are featured, incl...

Table of Contents:

• Preface
• 1. Preliminaries
• 2. Real, Cardinal and Ordinal Numbers
• 3. Elements of Topology
• 4. Measure Theory
• 5. Measurable Functions
• 6. Integration
• 7. Differentiation
• 8. Elements of Functional Analysis
• 9. Measures and Linear Functionals
• 10. Distributions
• 11. Functions of Several Variables
• Bibliography
• Index.