Difference between revisions of "Additive function"
From Encyclopedia of Mathematics
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Revision as of 18:12, 26 April 2012
finitely-additive function (on sets, on domains)
A real-valued function 
defined on a system of sets 
and such that
 | (*) |
for any finite number of pairwise-disjoint sets 
of 
whose union also belongs to 
. Countably-additive set functions are an important kind of additive functions (cf. Countably-additive set function).
Comments
Suppose that 
is a 
-algebra on a set 
. Then a non-negative function 
(taking, possibly, the value 
) on 
is an additive (finitely-additive, countably-additive) measure if it satisfies (*) for an arbitrary (respectively, finite, countable) number of disjoint sets 
in 
.
Usually, a measure (sic) is a countably-additive measure.
References
| [a1] | H.L. Royden, "Real analysis", Macmillan (1968) |
How to Cite This Entry:
Additive function. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Additive_function&oldid=19226
Additive function. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Additive_function&oldid=19226
This article was adapted from an original article by A.P. Terekhin (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article