Probability measure: Difference between revisions

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(explain distinction between prob measure and general measure, expand a bit on additivity)
[[File:AtomisationMaxwell-Cl-3D-vdWDistr.png|thumb|300px|In some cases, [[statistical physics]] uses ''probability measures'', but not all [[measure theory|measures]] 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>]]
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.
 
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