This text is designed for graduate-level courses in real analysis. Real Analysis, Fourth Edition, covers the basic material that every graduate student should know in the classical theory of functions of a real variable, measure and integration theory, an
PART I: LEBESGUE INTEGRATION FOR FUNCTIONS OF A SINGLE REAL VARIABLE 1. The Real Numbers: Sets, Sequences and Functions 1.1 The Field, Positivity and Completeness Axioms 1.2 The Natural and Rational Numbers 1.3 Countable and Uncountable Sets 1.4 Open