Infinite-dimensional Gaussian change of variables’ formula

In this paper, we study the Banach space ∞ of the bounded real sequences, and a measure N(a, ) over (R∞ , B∞ ) analogous to the finite-dimensional Gaussian law. The main result of our paper is a change of variables’ formula for the integration, with respect to N(a, ), of the measurable real functions on (E∞, B∞ (E∞)), where E∞ is the separable Banach space of the convergent real sequences. This change of variables is given by some (m, σ) functions, defined over a subset of E∞, with values on E∞, with properties that generalize the analogous ones of the finite-dimensional diffeomorphisms.