Measure and integration : a first course / M. Thamban Nair.

"A Chapman & Hall book."

Includes bibliographical references (page 199) and index.

Preface. Note to the Reader. Review of Riemann Integral. Lebesgue Measure. Measure and Measurable Functions. Integral of Positive Measurable Functions. Integral of Complex Measurable Functions. Integration on Product Spaces. Fourier Transform. References. Index.

This concise text is intended as an introductory course in measure and integration. It covers essentials of the subject, providing ample motivation for new concepts and theorems in the form of discussion and remarks, and with many worked-out examples.

The novelty of Measure and Integration: A First Course is in its style of exposition of the standard material in a student-friendly manner. New concepts are introduced progressively from less abstract to more abstract so that the subject is felt on solid footing. The book starts with a review of Riemann integration as a motivation for the necessity of introducing the concepts of measure and integration in a general setting. Then the text slowly evolves from the concept of an outer measure of subsets of the set of real line to the concept of Lebesgue measurable sets and Lebesgue measure, and then to the concept of a measure, measurable function, and integration in a more general setting. Again, integration is first introduced with non-negative functions, and then progressively with real and complex-valued functions. A chapter on Fourier transform is introduced only to make the reader realize the importance of the subject to another area of analysis that is essential for the study of advanced courses on partial differential equations.