Principles of real analysis - Aliprantis, Charalambos D (Academic Press, 1998)
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. The authors have included a new chapter on Hilbert Spaces as well as integrated over 150 new exercises throughout. This Third Edition covers the basic theory of integration in a clear, well-organized manner, using an imaginative and highly practical synthesis of the Daniel Method and the measure theoretic approach. Students will be challenged by the more than 600 exercises in the book. Topics are treated rigorously, illustrated by examples, offering a clear connection between real analysis and functional analysis.