A premeasure on an algebra or ring 
of subsets of a set 
is a set
function ![mu:S->[0,infty]](/images/equations/Premeasure/Inline3.svg)
such that 
and, for every disjoint sequence 
whose union belongs to 
,
 |
Premeasure
See also
Carathéodory Extension, Carathéodory Extension Theorem, Countable Additivity, Measurable Function, Measure, Measure Space, Outer MeasurePortions of this entry contributed by Christopher Stover
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References
Royden, H. L. and Fitzpatrick, P. M. Real Analysis. Pearson, 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