Borel measurability

Borel measurability

A function f is said to be Borel measurable provided its domain E is a Borel set and for each c, the set \displaystyle \{x\in E\mid f(x)>c\}=f^{-1}(c,\infty) is a Borel set.

Borel set

A Borel set is any set in a topological space that can be formed from open sets through the operations of countable union, countable intersection, and relative complement.

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