Definition:Measurable Set

Definition
Let $\struct {X, \Sigma}$ be a measurable space.

A subset $S \subseteq X$ is said to be ($\Sigma$-)measurable $S \in \Sigma$.

Also see

 * Outer Measure Restricted to Measurable Sets is Measure


 * Existence of Non-Measurable Subset of Real Numbers: from the axiom of choice, it is demonstrated that there exist non-measurable subsets of $\R$.