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[[File:MaxwellDistr.pngthumb300pxIn some cases, [[statistical physics]] uses ''probability measures'', but not all [[measure theorymeasures]] it uses are probability measures.<ref name=stern>''A course in mathematics for students of physics, Volume 2'' by Paul Bamberg, Shlomo Sternberg 1991 ISBN 0521406501 [http://books.google.com/books?id=eSmC4qQ0SCAC&pg=PA802 page 802]</ref><ref name= gut>''The concept of probability in statistical physics'' by Yair M. Guttmann 1999 ISBN 0521621283 [http://books.google.com/books?id=Q1AUhivGmyUC&pg=PA149 page 149]</ref>]]
{{Probability fundamentals}}
In mathematics, a '''probability measure''' is a [[realvalued 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 measuretheoretic probability'' by George G. Roussas 2004 ISBN 0125990227 [http://books.google.com/books?id=J8ZRgCNSwcC&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 "1 or 2" in a throw of a die should be the sum of the values assigned to "1" and "2".
