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Probability Measure


A probability measure P on a measurable space (S,S) is a measure on S with P(S)=1. The triple (S,S,P) is a probability space. Equivalently, P is said to be normalized.

A probability measure satisfies countable additivity. A finitely additive probability measure is only required to satisfy finite additivity, and its domain may be an algebra of sets (Juschenko 2015, p. 28).


See also

Finitely Additive Probability Measure, Measurable Space, Measure, Probability, Probability Space, Pushforward Measure, Radon Measure, State Space

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References

Juschenko, K. "Definitions of Amenability. First Examples." Ch. 4 in Amenability of Discrete Groups by Examples. Online manuscript, 2015. https://web.ma.utexas.edu/users/juschenko/files/Juschenko-Book-4.pdf.

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Probability Measure

Cite this as:

Weisstein, Eric W. "Probability Measure." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/ProbabilityMeasure.html

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