Radon measure [SEP] named after
Radon measure
In mathematics (specifically in measure theory), a Radon measure, named after Johann Radon, is a measure on the σ-algebra of Borel sets of a Hausdorff topological space "X" that is finite on all compact sets, outer regular on all Borel sets, and inner regular on open sets. These conditions guarantee that the measure is "compatible" with the topology of the space, and most measures used in mathematical analysis and in number theory are indeed Radon measures.
Motivation.
A
Radon–Nikodym theorem
In mathematics, the Radon–Nikodym theorem is a result in measure theory.
It involves a measurable space formula_1
on which two σ-finite measures are defined, formula_2 and formula_3.
It states that, if formula_4 (i.e. formula_3 is absolutely continuous with respect to formula_2), then there is a measurable function formula_7, such that for any measurable set formula_8,
The function is called the Radon–Nikodym derivative and is denoted by formula_10.
The theorem is named after Johann