Real Analysis and Functional Analysis

Author: Xu Shengzhi
Publisher:
Publish Date: 2006-09-01
Features: This book is a reference for undergraduate and graduate students studying real analysis and functional analysis. The real analysis part covers the first four chapters, focusing on the fundamental theories and methods of measure and integration. It includes: sets and relations, measures and measurable functions, integration and its properties, differentiation and indefinite integration. The functional analysis part covers the last four chapters, focusing on the fundamental theories and methods of point set analysis and linear operators. It includes: distance and point set analysis, bounded linear operators, geometry of inner product spaces, and spectral theory of linear operators. These two parts are important theoretical foundations for undergraduate and graduate students studying other mathematical and physical disciplines. The book summarizes the main theories and methods of real analysis and functional analysis. To help learners improve their ability to solve problems using set analysis, each section is equipped with examples and exercises, as well as solutions and hints for the exercises.