Real Analysis

This fourth edition of real analysis preserves the goal and general structure of its venerable predecessors to present the measure theory, integration theory and functional analysis that a modern analyst needs to know. New to this edition: this edition contains 50% more exercises than the previous edition. Fundamental results, including egoroff's theorem and urysohn's lemma are now proven in the text. The borel-cantelli lemma, chebychev's inequality, rapidly cauchy sequences and the continuity properties possessed both by measure and the integral are now formally presented in the text along with several other concepts