A note on functions which separate Gaussian measures
Assume that for any measurable function f and two Gaussian measures \(\mu\), \(\nu\) on Banach space E we have \[ \int f(x+y)\mu (dy)=\int f(x+y)\nu (dy)\quad for\quad every\quad x\in E. \] We give a sufficient condition on f which implies that \(\mu\) is a translation of \(\nu\). As a corollary we get that if a bounded function f has bounded support with non-empty interior then \(\mu =\nu\).
scientific article; zbMATH DE number 4056653