If 
is a sigma-algebra
and 
is a subset of 
, then 
is called measurable if 
is a member of 
. 
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.
Measurable Set
See also
Measurable Space, Sigma-AlgebraExplore with Wolfram|Alpha
Cite this as:
Weisstein, Eric W. "Measurable Set." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/MeasurableSet.html