Let $(X,\mathcal{M},\mu)$ be a complete [measure space](/page/Measure%20Space). Let $f:X\to\mathbb{R}$ be an $\mathcal{M}/\mathcal{B}(\mathbb{R})$-[measurable function](/page/Measurable%20Function), and let $g:X\to\mathbb{R}$ be a function. Suppose that $N:=\{x\in X:f(x)\ne g(x)\}$ belongs to $\mathcal{M}$ and satisfies $\mu(N)=0$. Then $g$ is $\mathcal{M}/\mathcal{B}(\mathbb{R})$-measurable.