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-Algebra## Explore with Wolfram|Alpha

## Cite this as:

Weisstein, Eric W. "Measurable Set." From
*MathWorld*--A Wolfram Web Resource. https://mathworld.wolfram.com/MeasurableSet.html