Sohrab H.H. Basic Real Analysis

Springer, 2014. — 683 p. — 2nd ed. — ISBN: 1493918400.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 functions of a real variable. The chapters on Lebesgue measure and integral have been rewritten entirely and greatly improved. They now contain Lebesgue’s differentiation theorem as well as his versions of the Fundamental Theorem(s) of Calculus. With expanded chapters, additional problems, and an expansive solutions manual, Basic Real Analysis, Second Edition is ideal for senior undergraduates and first-year graduate students, both as a classroom text and a self-study guide.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.
Lebesgue Measure and Integral in ℝ.
More on Lebesgue Integral and Measure.
General Measure and Probability.
Construction of Real Numbers.