Basic Real Analysis

• Main Author: Sohrab, Houshang H. (Author)
• Corporate Author: SpringerLink (Online service)
• Format: Electronic eBook
• Language: English
• Published: New York, NY : Springer New York : Imprint: Birkhäuser, 2014.
• Edition: 2nd ed. 2014.
• Subjects: Mathematics.; Measure theory.; Mathematical logic.; Measure and Integration.; Mathematical Logic and Foundations.

This expanded second edition presents the fundamentals and touchstone results of real analysis in full rigor, but in a style that requires little prior familiarity with proofs or mathematical language. The text is a comprehensive and largely self-contained introduction to the theory of real-valued f...

Table of Contents:

• Preface
• Set Theory
• Sequences and Series of Real Numbers
• Limits of Functions
• Topology of R and Continuity
• Metric Spaces
• The Derivative
• The Riemann Integral
• Sequences and Series of Functions
• Normed and Function Spaces
• The Lebesgue Integral
• Lebesgue Measure
• General Measure and Probability
• Appendix A: Construction of Real Numbers
• References
• Index.