Integration over an Infinite-Dimensional Banach Space and Probabilistic Applications

Abstract

We study, for some subsets I of N*, the Banach space E of bounded real sequences {xn}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.