© 2018

Real and Complex Analysis

Volume 1


Table of contents

  1. Front Matter
    Pages i-ix
  2. Rajnikant Sinha
    Pages 1-236
  3. Rajnikant Sinha
    Pages 237-390
  4. Rajnikant Sinha
    Pages 391-635
  5. Back Matter
    Pages 637-637

About this book


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.


Conformal Mapping Harmonic Functions Holomorphic Functions Fourier Transforms Lebesgue Integration

Authors and affiliations

  1. 1.VaranasiIndia

About the authors

RAJNIKANT SINHA is former professor of mathematics at Magadh University, Bodh Gaya, India. A passionate mathematician, Prof. Sinha has published numerous interesting research findings in international journals and books, including Smooth Manifolds (Springer) and the contributed book Solutions to Weatherburn’s Elementary Vector Analysis. His research focuses on topological vector spaces, differential geometry and manifolds.

Bibliographic information

  • Book Title Real and Complex Analysis
  • Book Subtitle Volume 1
  • Authors Rajnikant Sinha
  • DOI
  • Copyright Information Springer Nature Singapore Pte Ltd. 2018
  • Publisher Name Springer, Singapore
  • eBook Packages Mathematics and Statistics Mathematics and Statistics (R0)
  • Hardcover ISBN 978-981-13-0937-3
  • eBook ISBN 978-981-13-0938-0
  • Edition Number 1
  • Number of Pages IX, 637
  • Number of Illustrations 0 b/w illustrations, 0 illustrations in colour
  • Topics Analysis
  • Buy this book on publisher's site


“This introductory book should be useful to undergraduate students in mathematics and engineering. … The approach to each topic appears to have been carefully thought out, both as to the mathematical treatment and to the pedagogical presentation. The end result is a quite satisfactory book for undergraduate classroom use or even self-study.” (Christian Lavault, Mathematical Reviews, July, 2019)