A nonnegative function has integral zero if and only if it vanishes almost everywhere

A nonnegative function integrates to zero exactly when it vanishes almost everywhere.Suggest a slogan

Let $(X,\mcm,\mu)$ be a measure space and $f\in$ $L^+$. Then \[ \int_X f\dmu = 0 \quad\iff\quad f = 0 \ \mu\text{-almost everywhere}. \]