Nonabsolute Integration On Measure Spaces
World Scientific | English | 2018 | ISBN-10: 9813221968 | 160 pages | PDF | 2.70 mb
by Wee Leng Ng (Author)

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.

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