Measurable Set

If $F$ is a Sigma Algebra and $A$ is a Subset of $X$, then $A$ is called measurable if $A$ is a member of $F$. $X$ need not have, a priori, a topological structure. Even if it does, there may be no connection between the open sets in the topology and the given Sigma Algebra.

See also Measurable Space, Sigma Algebra