Metric outer measure

Summary

A metric outer measure is an outer measure on a metric space with one extra property. It is additive on any two sets lying at positive distance from each other. This condition links the outer measure with the geometry of the space. Its main use is that for a metric outer measure every Borel set is measurable in the sense of Carathéodory. Lebesgue outer measure and the Hausdorff outer measures are metric outer measures.