Countable Additivity (original) (raw)
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A set function 
possesses countable additivity if, given any countable disjoint collection of sets 
on which 
is defined,
A function having countable additivity is said to be countably additive.
Countably additive functions are countably subadditive by definition. Moreover, provided that 
where 
is the empty set, every countably additive function 
is necessarily finitely additive.
See also
Countable Additivity Probability Axiom, Countable Subadditivity,Disjoint Union, Finite Additivity, Set Function
This entry contributed by Christopher Stover
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References
Royden, H. L. and Fitzpatrick, P. M. Real Analysis. Pearson, 2010.
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Cite this as:
Stover, Christopher. "Countable Additivity." From MathWorld--A Wolfram Web Resource, created by Eric W. Weisstein. https://mathworld.wolfram.com/CountableAdditivity.html