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Finite Subadditivity


Finite subadditivity of a set function mu is the property that, for any finite collection of sets {E_k}_(k=1)^n on which mu is defined and whose union is in its domain,

 mu( union _(k=1)^nE_k)<=sum_(k=1)^nmu(E_k).

A set function possessing finite subadditivity is said to be finitely subadditive. In particular, every nonnegative finitely additive set function mu defined on an algebra of sets is also finitely subadditive.


See also

Countable Additivity, Countable Subadditivity, Disjoint Union, Finite Additivity, Set Function

Portions 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

Finite Subadditivity

Cite this as:

Weisstein, Eric W., with contributions by Christopher Stover. "Finite Subadditivity." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/FiniteSubadditivity.html

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