Measurable probability kernel
= Measurable probability kernel
{title2=$y\mapsto K_y$}
A family of probability measures $K_y$ on a measurable space for which $y\mapsto K_y(A)$ is measurable for every measurable set $A$. This combines measurable dependence on a parameter with a <probability measure> at each parameter. The <conditional measures of a factor> form such a kernel, with the additional fiber-support property from disintegration.