The book is divided into two parts. In the first part, integration theory is developed from the start in a general setting and immediately for vector-valued functions. This material can hardly be found in other textbooks. The second part covers various topics related to integration theory, such as spaces of measurable functions, convolutions, famous paradoxes, and extensions of formulae from elementary calculus to the setting of the Lebesgue integral.

Contents:

• Basic Integration Theory:
• Abstract Integration
• Adding a Topological Structure: The Radon Measure
• Adding a Group Structure: The Haar Measure
• Advanced Topics:
• Spaces of Measurable Functions
• Convolutions
• Connections with Logic and Set Theory
• Special Properties of the Lebesgue Measure
• Miscellaneous

"Because of the original treatment and selection of topics, the book stands out among the many books on the same subject. The author is to be commended for his efforts to enrich the existing literature on this subject with such an original book."

“Integration Theory: A Second Course does an admirable job at living up to its title … I like the author’s general approach ... I think most mathematicians will find it interesting.”

“… the book will serve its intended purpose.”

“... is a fine book on measure theory and integration, based on a general approach to the subject and discussing many difficult topics in the area. It can be recommended for advanced courses in measure theory, but it is suitable also for self-study for graduate students.”