Let $P = (\Omega, \mathcal{F}, \mathbb{}P)$ be a D1159: Probability space.
Let $X : \Omega \to [-\infty, \infty]$ be an D3066: Absolutely integrable random number on $P$ such that

(i)	$X =_{\mathsf{a.s.}} 0$

Then \begin{equation} \int_{\Omega} X \, d \mathbb{P} = 0 \end{equation}