Borel measure

Summary

A Borel measure on a topological space is a measure defined on the Borel sets, the sets generated by the open sets. It is the natural kind of measure on spaces such as $\R^n$, manifolds and topological groups, where open sets and continuous functions are given. Every continuous real function is measurable for a Borel measure. Some authors also require a Borel measure to be finite on compact sets.