Theory of Vector Integration

For many years a group of mathematicians has been working on the vector integration. This book is concerned with the different type of vector integration. A systematic description of the development of vector integration is given here. We discuss the integration theory for vector valued functions and scalar valued measures, scalar valued functions and vector valued measures, vector valued functions and vector valued measures. In chapter I we emphasize the Bochner integral and Pettis integral. In chapter II we give some basic properties of the space of all scalarly integrable functions and weakly scalarly integrable functions when the vector measure is defined on ¿-algebras. In chapter III we developed the same integration theory when the vector measure is defined on ¿-rings and analysed the differences between the L_1 spaces of vector measures defined on ¿-rings and defined on ¿-algebras. In chapter IV we introduce the idea of tensor integration theory and investigated many properties of the space of all tensor integrable functions.