Integration over an infinite-dimensional Banach space and probabilistic applications (Q1637834)

Summary: We study, for some subsets \(I\) of \(\mathbf N^*\), the Banach space \(E\) of bounded real sequences \(\{x_n\}_{n\in I}\). For any integer \(k\), we introduce a measure over \((E,\mathcal B(E))\) 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.