This book presents a unified treatise of the theory of measure and integration. In the setting of a general measure space, every concept is defined precisely and every theorem is presented with a clear and complete proof with all the relevant details. Counter-examples are provided to show that certain conditions in the hypothesis of a theorem cannot be simply dropped.

The dependence of a theorem on earlier theorems is explicitly indicated in the proof, not only to facilitate reading but also to delineate the structure of the theory. The precision and clarity of presentation make the book an ideal textbook for a graduate course in real analysis while the wealth of topics treated also make the book a valuable reference work for mathematicians.

Contents:

• Measure Spaces
• The Lebesgue Integral
• Differentiable and Integration
• The Classical Banach Spaces
• Extension of Additive Set Functions to Measures
• Measure and Integration on the Euclidean Space
• Hausdorff Measures on the Euclidean Space

“Finally, I recommend this book for a student who is helped by a good adviser.”

Reviews of the First Edition

“This book is well organized and the statements and proofs of the results are done very carefully.”

“Every concept is defined precisely and every theorem is presented with a detailed and complete proof. Counter-examples are presented to show that certain conditions in the hypothesis of a theorem cannot be simply dropped.”

“It is particularly suitable for a one-year course at the graduate level.”