Set function

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A mapping of a certain collection of subsets of a given set into another set, usually into the real numbers or the complex numbers . An important class of set functions are the additive set functions, for which

 (*)

and the -additive set functions, which satisfy equation (*) for a countably infinite collection of sets also (replace by ). If takes only non-negative values, , and is a -algebra, then is called a measure.

References

 [1] L.V. Kantorovich, G.P. Akilov, "Functional analysis" , Pergamon (1982) (Translated from Russian)