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Real and Complex Analysis

Volume 1

  • Rajnikant Sinha

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

Introduction

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.

Keywords

Conformal Mapping Harmonic Functions Holomorphic Functions Fourier Transforms Lebesgue Integration

Authors and affiliations

  • Rajnikant Sinha
    • 1
  1. 1.VaranasiIndia

Bibliographic information