Comparaison de mesures gaussiennes et de mesures produit
The author proves the following: let \(\xi =(\xi_ i)\), \(\eta =(\eta_ i)\) be two random variables with values in \({\mathbb{R}}^{\infty}={\mathbb{R}}\times {\mathbb{R}}\times..\). such that \(\xi\) is Gaussian, the \(\eta_ i's\) are independent and law \((\xi_ i)\) equivalent to law \((\eta_ i)\), \(i=1,2,...\); then the following are equivalent: (i) law (\(\xi)\) is not orthogonal to law (\(\eta)\); (ii) law (\(\xi)\) is equivalent to law (\(\eta)\); (iii) law (\(\xi)\) and law (\(\eta)\) are equivalent to the product measure \(\otimes_ i\) law \((\xi_ i)\). Besides the intrinsic interest of the theorem, the technique of proof used is significant.
scientific article; zbMATH DE number 3852133