Definition:Borel Sigma-Algebra/Also known as

Definition
The Borel $\sigma$-algebra is also found with the name topological $\sigma$-algebra, or even just $\sigma$-algebra.

When the set $S$ or the topology $\tau$ are clear from the context, one may encounter $\map \BB \tau$, $\map \BB S$ or even just $\BB$.

Some authors write $\BB^n$ for $\map \BB {\R^n, \tau}$.