A quasi-Borel space (QBS) is a set equipped with a notion of random variable, providing a model of measurable space suitable for probability theory. The advantage of quasi-Borel spaces over traditional formulations is that they provide a nice category of measurable spaces: it is cartesian closed, and the set of probability measures of a QBS forms a QBS.
A quasi-Borel space consists of an underlying set and a set of functions satisfying:
The category of quasi-Borel spaces can be used as a denotational semantics for higher-order probabilistic programming languages?.
The category of quasi-Borel spaces is the category of concrete sheaves on the category of standard Borel spaces considered with the extensive coverage. As such, quasi-Borel spaces form a Grothendieck quasitopos. (A standard Borel space is a measurable space that is a retract of , equivalently, it is a measurable space that comes from a Polish space, equivalently, it is either isomorphic to or countable, discrete and non-empty.)
Quasi-Borel spaces were introduced in
Last revised on May 29, 2020 at 01:29:00. See the history of this page for a list of all contributions to it.