Differentiation Theory over Infinite-Dimensional Banach Spaces

Abstract

We study, for any positive integerkand for any subsetIofN⁎, the Banach spaceEIof the bounded real sequencesxnn∈Iand a measure overRI,B(I)that generalizes thek-dimensional Lebesgue one. Moreover, we expose a differentiation theory for the functions defined over this space. The main result of our paper is a change of variables’ formula for the integration of the measurable real functions onRI,B(I). This change of variables is defined by some infinite-dimensional functions with properties that generalize the analogous ones of the standard finite-dimensional diffeomorphisms.