Probability measure: Difference between revisions

The [[conditional probability]] based on the intersection of events defined as:
 
:<math>P\mu (B \mid A) = \frac{P\mu(A \cap B)}{P\mu(A)}.</math>
 
satisfies the probability measure requirements so long as <math>P\mu(A)</math> is not zero.<ref>''Probability, Random Processes, and Ergodic Properties'' by Robert M. Gray 2009 {{isbn|1-4419-1089-1}} [https://books.google.com/books?id=x-VbL8mZWl8C&pg=PA163 page 163]</ref>
 
Probability measures are distinct from the more general notion of [[Fuzzy measure theory|fuzzy measures]] in which there is no requirement that the fuzzy values sum up to 1, and the additive property is replaced by an order relation based on [[set inclusion]].
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