Standard Borel probability space ($(X,\mathcal{B},\mu )$)

A probability space whose measurable space is isomorphic to a Borel subset of a complete separable metric space with its Borel sigma-algebra. This supplies a countable generating algebra and permits the disintegration theorem for a probability measure. Completions can be handled modulo null sets; conditional kernels are chosen on the underlying Borel model.