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Countable Subadditivity


A set function mu is said to possess countable subadditivity if, given any countable disjoint collection of sets {E_k}_(k=1)^n on which mu is defined,

 mu( union _(k=1)^inftyE_k)<=sum_(k=1)^inftymu(E_k).

A function possessing countable subadditivity is said to be countably subadditive.

Any countably subadditive function mu is also finitely subadditive presuming that mu(emptyset)=0 where emptyset is the empty set.


See also

Disjoint Union, Finite Subadditivity, Set Function

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. "Countable Subadditivity." From MathWorld--A Wolfram Web Resource, created by Eric W. Weisstein. https://mathworld.wolfram.com/CountableSubadditivity.html

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