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Premeasure


Let S be a collection of subsets of a set X and let mu:S->[0,infty] be a set function. The function mu is called a premeasure provided that mu is finitely additive, countably monotone, and that mu(emptyset)=0 if emptyset in S, where emptyset is the empty set.


See also

Countable Monotonicity, Finite Additivity, Measurable Function, Measure, Measure Space, Outer Measure

This entry contributed by Christopher Stover

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References

Royden, H. L. and Fitzpatrick, P. M. Real Analysis. Pearson, 2010.

Cite this as:

Stover, Christopher. "Premeasure." From MathWorld--A Wolfram Web Resource, created by Eric W. Weisstein. https://mathworld.wolfram.com/Premeasure.html

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