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Principles of Real Analysis,
Charalambos Aliprantis, Owen Burkinshaw
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.
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