On Gaussian conditional measures depending on a parameter

Georgii A. Alekseev, Ekaterina V. Yurova

Department of Mechanics and Mathematics, Moscow Stats University, 119991 Moscow, Russia

Abstract: We prove that if a family of Gaussian measures $\mu_\alpha$ on the product of two Souslin locally convex spaces $X$ and $Y$ depends measurably on a parameter $\alpha$, then it is possible to find conditional measures $\mu_\alpha^y$ on $X$ jointly measurable in $y$ and $\alpha$.

Keywords: Gaussian measure, conditional measure, measurable dependence on a parameter.

MSC: 28C20, 46G12, 60B11

Language: English

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