Markov kernel

Summary

A Markov kernel from a space $X$ to a space $Y$ assigns to each point of $X$ a probability measure on $Y$. The assignment must be measurable in the point. It generalises the transition matrix of a Markov chain to arbitrary state spaces. Kernels describe random transitions, conditional distributions and randomised maps. They can be composed, and together with a starting measure they build measures on product spaces.