A useful property is the following. Assume is a measurable map from to and is a measurable map from to If there exists a measurable map from to such that for all then If is finite or countably infinite or, more generally, is a standard Borel space (for example, a separable complete metric space with its associated Borel sets), then the converse is also true. Examples of standard Borel spaces include with its Borel sets and with the cylinder σ-algebra described below.
A useful property is the following Assume is a measurable map from to and is a measurable map from to If there exists a measurable map from to such that for all then If is finite or countably infinite or more generally is a standard Borel space (for example a separable complete metric space with its associated Borel sets) then the converse is also true Examples of standard Borel spaces include with its Borel sets and with the cylinder σ-algebra described below