Probability measure: Difference between revisions

just clarifying the events don't necessarily form the entire set
(just clarifying the events don't necessarily form the entire set)
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 0125990227 [http://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 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 "Heads1 or Tails2" in a cointhrow tossof a die should be the sum of the values assigned to Heads"1" and Tails"2".
 
Probability measures have applications in diverse fields, from physics to finance and biology.
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