Real and Complex Analysis: Volume 1 by Rajnikant Sinha (PDF)

Description

This is the first volume of the two-volume book on real and complex analysis. This volume is an introduction to measure theory and Lebesgue measure where the Riesz representation theorem is used to construct Lebesgue measure. Intended for undergraduate students of mathematics and engineering, it covers the essential analysis that is needed for the study of functional analysis, developing the concepts rigorously with sufficient detail and with minimum prior knowledge of the fundamentals of advanced calculus required. Divided into three chapters, it discusses exponential and measurable functions, Riesz representation theorem, Borel and Lebesgue measure, -spaces, Riesz–Fischer theorem, Vitali–Caratheodory theorem, the Fubini theorem, and Fourier transforms. Further, it includes extensive exercises and their solutions with each concept. The book examines several useful theorems in the realm of real and complex analysis, most of which are the work of great mathematicians of the 19th and 20th centuries.

User’s Reviews

Reviews from Amazon users which were colected at the time this book was published on the website:

⭐This book is nearly perfect for self-study of real and complex analysis at graduate level. Solutions are given to the problems, which makes self-study much easier (at graduate level), which is quite appreciable nowadays. The main drawback is the lack of an index, which I think is quite essential for such a book. This is why I rated it “only” four stars instead of five. Its companion volume has the same drawback.

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