Real Analysis is indispensable for in-depth understanding and effective application of methods of modern analysis. The book is aimed at graduate students of mathematics and related disciplines wishing to learn the basics and techniques of Real Analysis with reasonable ease.

• 1: Introduction and Preliminaries


• 2: A Glimpse of Measure and Integration


• 3: Construction of Measures


• 4: Functions of Real Variables


• 5: Basic Principles of Linear Analysis


• 6: Lp Spaces


• 7: Fourier Integral and Sobolev Space Hs


• 8: Postscript

Fon-Che Liu received a first degree in Mathematics from Taiwan University (1962) and Ph.D. degree from Purdue University (1968). He joined the Institute of Mathematics, Academia Sinica in 1971 as Associate Research Fellow and was promoted to Research Fellow in 1973. He was Professor of Mathematics at Taiwan University between 1974 and 2005, and has been Visiting Professor at Purdue University and Wayne State University. Until 2000 he held the role of Director, Institute of Mathematics, Academia Sineca-Taipei, and was President of the Chinese Mathematical Society Taipei in the early 1990s.