Radon measure

In the mathematical field of measure theory radon measurements are (named after Johann Radon ) measure on the Borel σ - algebra of a Hausdorff space with certain regularity properties. The term is not used consistently in the literature.

A definition (of Laurent Schwartz) is:

It is locally finite: for each there exists an open environment. " From the inside regularly " means: for all measurable quantities.

Examples of measures with this Regularitätseigenschaft are:

• The Lebesgue - Stieltjes measure on the Borel sets of are exactly the radon measurements.
• The hair - measure on locally compact Hausdorff topological groups.

To the notion of Radon measure to get in a natural way when one examines positive linear functionals " " (so-called Radon integrals) on ( the continuous, real-valued functions with compact support ) on a locally compact Hausdorff space. In such locally compact spaces the property of local finiteness of a measure is equivalent to finiteness of the measure on compact sets (see Borel measure ).