Probability measure: Difference between revisions

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In mathematics, a '''probability measure''' is a [[real-valued function]] defined on a set of events in a [[probability space]] 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 [ 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 probability space.
Intuitively, the additivity property says that the probability assigned to the union of two disjoint events by the measure should be the sum of the probabilities of the events, e.g. the value assigned to "1 or 2" in a throw of a diedice should be the sum of the values assigned to "1" and "2".
Probability measures have applications in diverse fields, from physics to finance and biology.