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In mathematics, a probability measure is a real-valued function defined on a set of events in a probability space that satisfies measure properties such as countable additivity.
The requirements for a function
{\displaystyle \mu }
to be a probability measure on a probability space are that:
For example, given three elements 1, 2 and 3 with probabilities
1
index /
4
,
1
/
4
{\displaystyle 1/4,1/4}
and
1
/
2
,
{\displaystyle 1/2,}
the value assigned to
link
{
1
,
3
}
{\displaystyle \{1,3\}}
is
1
/
4
+
1
/
2
=
3
/
4
,
{\displaystyle 1/4+1/2=3/4,}
as in the diagram on the right.
The conditional probability based on the intersection of events see page as:
Probability measures are distinct from the more general notion of fuzzy measures in which there is no requirement that the fuzzy values sum up to
1
,
{\displaystyle 1,}
and the additive property is replaced by an order relation based on set inclusion. .