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.
|||L.V. Kantorovich, G.P. Akilov, "Functional analysis" , Pergamon (1982) (Translated from Russian)|
|[a1]||N. Dunford, J.T. Schwartz, "Linear operators. General theory" , 1 , Interscience (1958)|
Set function. Encyclopedia of Mathematics. URL: http://www.encyclopediaofmath.org/index.php?title=Set_function&oldid=15370