Let 
be a collection
of subsets of a set 
and let ![mu:S->[0,infty]](/images/equations/Premeasure/Inline3.svg)
be a set function.
The function 
is called a premeasure provided that 
is finitely additive,
countably monotone, and that 
if 
, where 
is the empty set.
Premeasure
See also
Carathéodory Extension, Carathéodory Extension Theorem, Countable Monotonicity, Finite Additivity, Measurable Function, Measure, Measure Space, Outer MeasureThis 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