Set function
From Encyclopedia of Mathematics
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) |
Comments
References
| [a1] | N. Dunford, J.T. Schwartz, "Linear operators. General theory" , 1 , Interscience (1958) |
How to Cite This Entry:
Set function. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Set_function&oldid=28010
Set function. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Set_function&oldid=28010
This article was adapted from an original article by V.I. Sobolev (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article