Suppose we have the sequence of measurable functions $\displaystyle (f_n) $ convergence in measure to $\displaystyle f $ on $\displaystyle X \subseteq \mathbb{R}. $ Prove that for all $\displaystyle \alpha >0$,there exists $\displaystyle P_\alpha \in \mathbb{N}$ such that for all $\displaystyle n\ge P_\alpha$ , $\displaystyle m(\{ x\in X:|f_n(x)-f(x)|\ge \alpha\})\le \alpha$.