On dependence of solutions to Fokker–Planck–Kolmogorov equations on their coefficients and initial data

We consider the Cauchy problem for the Fokker–Planck–Kolmogorov equation where the coefficients and the initial data depend measurably on a parameter and show that there is a selection of a solution measurable with respect to the parameter. In particular, the coefficients and the initial data themselves can be regarded as parameters. Several settings of the problem are discussed in which the measurability of solutions with respect to parameters is established.