Borel measure
Let formula_1 be a locally compact Hausdorff space, and let formula_2 be the smallest σ-algebra that contains the open sets of formula_1; this is known as the σ-algebra of Borel sets. A Borel measure is any measure formula_4 defined on the σ-algebra of Borel sets. A few authors require in addition that formula_4 is locally finite, meaning that formula_6 for every compact set formula_7. If a Borel measure formula_4 is both inner regular and outer regular, it is called a regular Borel measure. If formula_4 is both inner regular, outer regular, and locally finite, it is called a Radon measure.