 Measurable function

A function $f:(X,\mathcal{A})\to (Y,\mathcal{B})$ between measurable spaces is measurable when $f^{-1}(B)\in \mathcal{A}$ for every $B\in \mathcal{B}$.

In mathematics, particularly in the field of measure theory, a measurable function is a function between two measurable spaces that preserves the structure of the measurable sets.