Integration having values in a banach space

The paper is a report on some work of Bartle, Dunford, and Schwartz on a generalization of the Lebesgue Integral and also includes some related material. In the first part of the paper, a measure space (S, E) with the positive measure v defined on it is discussed and a number of its properties are derived. Then the properties of the space of measures which are of finite variation on this space are discussed. In the final part of the paper, a generalized Lebesgue integration is defined and many of the usual properties of the Lebesgue integral are shown to hold, the final result being the bounded convergence theorem.