The countable additivity probability axiom states that a probability measure 
satisfies
for every sequence of pairwise disjoint events 
in its probability space
(Hunter 2011, p. 5).
The corresponding finite additivity formula
is
It follows by taking all remaining events in the sequence to be the empty set, whose probability
is zero.
See also
Countable Additivity,
Countable Set
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References
Hunter, J. K. "Measures." §1.6 in Measure Theory. p. 5, 2011. https://www.math.ucdavis.edu/~hunter/measure_theory/measure_notes.pdf.Referenced
on Wolfram|Alpha
Countable Additivity
Probability Axiom
Cite this as:
Weisstein, Eric W. "Countable Additivity Probability
Axiom." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/CountableAdditivityProbabilityAxiom.html
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