Borel measure

As a Borel measure (after Émile Borel ) is called in the mathematical field of measure theory those dimensions on the borel σ - algebra between a Hausdorff space, for which:

This property is called local finiteness. If the space is locally compact, corresponding to local finiteness of the requirement that μ on compact sets is finite.

A special case is the Lebesgue - Borel measure.

Other meanings

The term is not used consistently in the literature. Sometimes also

• Outer dimensions with respect to which all Borel sets are measurable
• The measure on the borel σ - algebra on between which each interval assigns the measure

Called a Borel measure.