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, RieszFischer theorem, VitaliCaratheodory 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 arethe work of great mathematicians of the 19th and 20th centuries.

Discusses major topics in real and complex analysis Includes the essential analysis that is needed for the study of functional analysis Presents applications of complex analysis to analytic number theory Features over 800 step-by-step, fully solved examples Is useful to undergraduate students of mathematics and engineering

Autorentext
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.

Inhalt
Chapter 1. Lebesgue Integration.- Chapter 2. Lp-Spaces.- Chapter 3. Fourier Transforms.- Chapter 4 . Holomorphic and Harmonic Functions.- Chapter 5 . Conformal Mapping.- Chapter 6 . Analytic Continuation.- Chapter 7 . Special Functions. <p