Differentiation Theory over Infinite-Dimensional Banach Spaces

We study, for any positive integer k and for any subset I of N⁎, the Banach space EI of the bounded real sequences xnn∈I and a measure over RI,B(I) that generalizes the k-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 on RI,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