This volume presents a motivated introduction to a subject that goes under various headings such as real analysis, Lebesgue measure and integration, measure theory, modern analysis, advanced analysis etc. A prerequisite for the text is a first course in mathematical analysis. The text can be used for a one-year course in the topic. Due to the lecture-notes style of the text, it would also be appropriate to use for individual self-study.

Synopsis

The book aims at developing the concepts and techniques of measure theory. Starting with a review of Riemann integral and its drawbacks, Lebesgue integral and integration over general measure spaces is developed in a systematic and logical manner. The book is written in a lecture style so as to make the subject matter easily accessible to students. Historical notes on the notion of integral are included to give the reader an insight into the development of the subject. Exercises are interwoven in the text following the concept/theorem needed to solve them. The book is self-contained and presumes only the knowledge of a standard first course in Mathematical Analysis. The topics covered in the book also prepare the reader for advanced studies in diverse branches of analysis like functional analysis and harmonic analysis.

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