Measure and Integration: A First Course

1st Edition

M Thamban Nair

Chapman and Hall/CRC
November 18, 2019 Forthcoming
Textbook - 216 Pages
ISBN 9780367348397 - CAT# 322114

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Summary

This concise text is intended for 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 also with many worked-out examples.

The novelty of this book 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 feeling of the subject can be on solid footings. The book starts with a review of Riemann integration as a motivation for the necessity for 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 introduced first for non-negative functions, and then progressively for 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 which is essential for the study of advanced courses on partial differential equations.

Key Features

  • Numerous examples are worked out in detail.
  • Exercises are interspersed throughout the book to aid the students’ understanding.
  • Lebesgue measurability is introduced only after convincing the reader of its necessity.
  • Integral of a non-negative measurable function is defined after motivating its existence as limits of integrals of simple measurable functions.
  • Several inquisitive questions and important conclusions are displayed prominently.
  • A good number of problems with liberal hints are provided at the end of each chapter.

The book is so designed that it can be used as a text for a one-semester course in the first year of the master program in mathematics or at the senior undergraduate level.

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