Regular Borel measure
= Regular Borel measure
A finite positive <Borel measure> on a <compact Hausdorff space> is regular when its values on Borel sets can be approximated from inside by compact sets and from outside by open sets. For signed or complex measures require this property of the <variation measure>. These are the measures representing the <continuous dual space> of $C(K)$ in the <Riesz-Markov-Kakutani representation theorem>.