V K Jain | Akateeminen Kirjakauppa

This is the second edition of a successful textbook intended to provide a basic course in Lebesgue measure and integration for honours and post graduate students. Meticulous care has been taken to give detailed explanations of the reasons of worked content and of the methods used, together with numerous examples and counter examples throughout the book.
Each topic has been presented in an easy, lucid style, for ease of understanding. The material has been arranged by sections, spread through seven chapters. The book opens with a chapter on preliminaries discussing basic concepts and results which will be taken for granted later in the text. It is followed by chapters on Infinite Sets, Measurable Sets, Measurable Functions, Lebesgue Integral, Differentiation and Integration, and the Lebesgue Lp Spaces, a chapter that will lend itself to applications within the field of functional analysis. Each chapter also contains a set of graded problems, with hints where necessary to help find the solutions.

Contents:
Preliminaries
Infinite Sets
Measurable Sets
Measurable Functions
Lebesgue Integral
Differentiation and Integration
Lebesgue Lp Spaces