On Gaussian conditional measures depending on a parameter

Georgii A. Alekseev, Ekaterina V. Yurova
Theory of Stochastic Processes
Vol.22 (38), no.2, 2017, pp.1-7
We prove that if a family of Gaussian measures μ_α on the product of two Souslin locally convex spaces X and Y depends measurably on a parameter α, then it is possible to find conditional measures μ_α^y on X jointly measurable in y and α.