Measurable function

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In mathematics, a function f that maps each element of a measurable space \scriptstyle (X,\mathcal{F}_X) to an element of another measurable space \scriptstyle (Y,\mathcal{F}_Y) is said to be measurable (with respect to the sigma algebra \scriptstyle \mathcal{F}_X) if for any set \scriptstyle A \in \mathcal{F}_Y it holds that \scriptstyle f^{-1}(A) \in \mathcal{F}_X, where \scriptstyle f^{-1}(A)=\{x \in X \mid f(x) \in A\}.

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