 Positive part of a real-valued function

The positive part of a real-valued function $f$ is $f_{+}(x)=\max (0,f(x))$. Together with the negative part $f_{-}(x)=\max (0,-f(x))$, it gives $f=f_{+}-f_{-}$ and $|f|=f_{+}+f_{-}$.