Introduction

This book offers to the reader a self-contained treatment and systematic exposition of the real-valued theory of a nonabsolute integral on measure spaces. It is an introductory textbook to Henstock-Kurzweil type integrals defined on abstract spaces. It contains both classical and original results that are accessible to a large class of readers.

Key Challenges

It is widely acknowledged that the biggest difficulty in defining a Henstock-Kurzweil integral beyond Euclidean spaces is the definition of a set of measurable sets which will play the role of ''intervals'' in the abstract setting.

Innovative Approach

In this book the author shows a creative and innovative way of defining ''intervals'' in measure spaces, and proves many interesting and important results including the well-known Radon-Nikodým theorem.