Probability measure: Difference between revisions

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{{Use American English|date = March 2019}}
{{Short description|Measure of total value one, generalizing probability distributions}}
[[File:Maxwell-Distr.png|thumb|300px|In many 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|0-521-40650-1}} [https://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|0-521-62128-3}} [https://books.google.com/books?id=Q1AUhivGmyUC&pg=PA149 page 149]</ref>]]<br />{{Probability fundamentals}}
{{Probability fundamentals}}
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}} [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 probability space.