Editing Probability measure (section)

{{Short description|Measure of total value one, generalizing probability distributions}}
{{Use American English|date = March 2019}}
{{Probability fundamentals}}
In [[mathematics]], a '''probability measure''' is a [[real-valued function]] defined on a set of events in a [[σ-algebra]] that satisfies [[Measure (mathematics)|measure]] properties such as ''countable additivity''.<ref>''An introduction to measure-theoretic probability'' by George G. Roussas 2004 {{isbn|0-12-599022-7}} [https://books.google.com/books?id=J8ZRgCNS-wcC&pg=PA47 page 47]</ref>  The difference between a probability measure and the more general notion of measure (which includes concepts like [[area]] or [[volume]]) is that a probability measure must assign value 1 to the entire space.

Intuitively, the additivity property says that the probability assigned to the union of two disjoint (mutually exclusive) events by the measure should be the sum of the probabilities of the events; for example, the value assigned to the outcome "1 or 2" in a throw of a dice should be the sum of the values assigned to the outcomes "1" and "2".

Probability measures have applications in diverse fields, from physics to finance and biology.