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.
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