In mathematics, a **standard Borel space** is the Borel space associated with a Polish space. Except in the case of discrete Polish spaces, the standard Borel space is unique, up to isomorphism of measurable spaces.

A measurable space is said to be "standard Borel" if there exists a metric on that makes it a complete separable metric space in such a way that is then the Borel σ-algebra.^{[1]}
Standard Borel spaces have several useful properties that do not hold for general measurable spaces.

- If and are standard Borel then any bijective measurable mapping is an isomorphism (that is, the inverse mapping is also measurable). This follows from Souslin's theorem, as a set that is both analytic and coanalytic is necessarily Borel.
- If and are standard Borel spaces and then is measurable if and only if the graph of is Borel.
- The product and direct union of a countable family of standard Borel spaces are standard.
- Every complete probability measure on a standard Borel space turns it into a standard probability space.

**Theorem**. Let be a Polish space, that is, a topological space such that there is a metric on that defines the topology of and that makes a complete separable metric space. Then as a Borel space is Borel isomorphic to one of
(1) (2) or (3) a finite discrete space. (This result is reminiscent of Maharam's theorem.)

It follows that a standard Borel space is characterized up to isomorphism by its cardinality,^{[2]} and that any uncountable standard Borel space has the cardinality of the continuum.

Borel isomorphisms on standard Borel spaces are analogous to homeomorphisms on topological spaces: both are bijective and closed under composition, and a homeomorphism and its inverse are both continuous, instead of both being only Borel measurable.