Integration over an Infinite-Dimensional Banach Space and Probabilistic Applications

In this paper we study, for some subsets I of N^{∗}, the Banach space E of bounded real sequences {x_{n}}_{n∈I}. For any integer k, we introduce a measure over (E,B(E)) that generalizes the k-dimensional Lebesgue measure; consequently, also a theory of integration is defined. The main result of our paper is a change of variables formula for the integration