Conditional measures of a factor
= Conditional measures of a factor
{title2=$\mu_y$}
= Conditional measure
{synonym}
The fiber-supported <measurable probability kernel> supplied by the <disintegration theorem for a probability measure> for a <factor map>. For integrable $f$, $\mathbb E[f\mid\varphi^{-1}\mathcal B_Y](x)=\int f\,d\mu_{\varphi(x)}$ <almost everywhere>. The same construction applies to general measurable maps and countably generated sub-sigma-algebras modulo null sets.