# 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.

## Author: mathtuition88

https://mathtuition88.com/

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