A premeasure on an algebra of sets or ring of sets 
of subsets of a set 
is a set function ![mu:S->[0,infty]](/images/equations/Premeasure/Inline3.svg)
such that 
and, for every sequence
of pairwise disjoint sets 
whose union belongs
to 
,
 |
Premeasure
See also
Algebra of Sets, Carathéodory Extension, Carathéodory Extension Theorem, Countable Additivity, Measure, Measure Space, Outer Measure, Ring of SetsPortions of this entry contributed by Christopher Stover
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References
Royden, H. L. and Fitzpatrick, P. M. Real Analysis, 4th ed. Boston, MA: Pearson-Prentice Hall, 2010.Referenced on Wolfram|Alpha
PremeasureCite this as:
Weisstein, Eric W., with contributions by Christopher Stover. "Premeasure." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/Premeasure.html