= Negative part of a real-valued function
{title2=$f_-(x)=\max(0,-f(x))$}
= Negative part
{synonym}
The <negative part> of a <real-valued function> $f$ is the nonnegative <function> $f_-(x)=\max(0,-f(x))$. It records the magnitude of the negative values, rather than retaining their sign: if $f(x)=-3$, then $f_-(x)=3$. Together with the <positive part>, it gives $f=f_+-f_-$ and $|f|=f_++f_-$. This decomposition defines the <Lebesgue integral> of a signed <function> and makes the <integrability> condition explicit.
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