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Countable Subadditivity


Countable subadditivity of a set function mu is the property that, for any countable collection of sets {E_k}_(k=1)^infty for which mu is defined both on each E_k and on their union,

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

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

Any countably subadditive set 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

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

Countable Subadditivity

Cite this as:

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

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