Use this tag for questions related to Borel measures, which, on a topological space, are measures defined on all open sets.
A Borel measure on a topological space is a measure defined on all open sets (and thus on all Borel sets).
Formally, let X be a locally-compact Hausdorff space, and let $\mathfrak B$(X) be the smallest $\sigma$-algebra that contains the open sets of X, which is called the $\sigma$-algebra of Borel sets. A Borel measure is any measure $\mu$ defined on the $\sigma$-algebra of Borel sets. Some authors require also that $\mu$ be locally compact, meaning that $\mu$(C) < $\infty$ for every compact set C. If a Borel measure $\mu$ is inner regular and outer regular, it is called a regular Borel measure (some authors also require it to be tight). If $\mu$ is inner regular and locally finite, it is called a Radon measure.
