Convergence in measure

Let \(m\) be Lebesgue measure on \(\RR^n\), let \(E\subseteq\RR^n\) be Lebesgue measurable, and let \(f_k\colon E\to\RR\) for \(k\geq 1\) and \(f\colon E\to\RR\) be measurable. The sequence \((f_k)\) converges in measure to \(f\) on \(E\) if for every \(\alpha>0\), \[ \lim_{k \to \infty} m\qty{\theset{x \in E \suchthat \abs{f_{k}(x)-f(x)}>\alpha}}=0. \]