Principles of Real Analysis

With the success of its previous editions, Principles of Real Analysis, Third Edition, continues to introduce students to the fundamentals of the theory of measure and functional analysis. In this thorough update, the authors have included a new chapter on Hilbert spaces as well as integrating over 150 new exercises throughout. The new edition covers the basic theory of integration in a clear, well-organized manner, using an imaginative and highly practical synthesis of the "Daniell Method" and the measure theoretic approach. Students will be challenged by the more than 600 exercises contained in the book. Topics are illustrated by many varied examples, and they provide clear connections between real analysis and functional analysis.

Gives a unique presentation of integration theoryOver 150 new exercises integrated throughout the textPresents a new chapter on Hilbert SpacesProvides a rigorous introduction to measure theoryIllustrated with new and varied examples in each chapterIntroduces topological ideas in a friendly mannerOffers a clear connection between real analysis and functional analysisIncludes brief biographies of mathematicians

Fundamentals of Real Analysis
Topology and Continuity
The Theory of Measure
The Lebesgue Integral
Normed Spaces and Lp-Spaces
Hilbert Spaces
Special Topics in Integration
Bibliography