NONABSOLUTE INTEGRATION ON MEASURE SPACES

 ,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&ndash,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&ndash,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&ndash,Nikodý,m theorem._,