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.
See alsoMeasurable Space, Sigma-Algebra
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Weisstein, Eric W. "Measurable Set." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/MeasurableSet.html