Real variable function

Author: Hu Shigeng
Publisher:
Publish Date: 1999-07-01
Features: The book consists of five chapters. The first two chapters (Sets and Point Sets, Measure and Measurable Functions) concisely introduce the foundational knowledge of set theory and measure theory required for the entire book. Chapter 3 covers Lebesgue Integration, and Chapter 4, Lp Spaces, forms the central content of the book, systematically introducing Lebesgue integration theory and providing numerous application examples. Chapter 5 discusses Differential Theory and Stieltjes Integration, including an overview of generalized measures. The book includes remarks at the end of each chapter and exercises divided into two categories (A and B) based on difficulty. Additionally, solutions and hints for every exercise are provided at the end of the book. Compared to traditional textbooks, this book appropriately increases the number of application examples, adds more exercises, and separates basic from advanced problems. It also strengthens explanations of background and key ideas, adds guiding notes at the transitions between chapters, and ensures precise and clear language. The book can serve as a textbook or reference for mathematics and related disciplines in universities and higher normal schools, as well as for self-study by readers with a certain mathematical foundation.