Definition of $\log^- $ function

Question

Can anyone tell me the definition of the $\log^- $ function ? Or give reference where I can also find its properties? I know the analogous $\log^+$ function which is defined as $\log^+ x= \log x$ if $x\geq 1$ and $0 $ if $0\leq x<1.$

Answer 1

The following is a more or less standard notation. For a function $f\colon D\to\Bbb R$ $$ f^+(x)=\max(f(x),0),\quad f^-(x)=\min(f(x),0). $$ $f^+$ and $f^-$ are known as the positive and negative part of $f$.

Then $$ \log^-x=\begin{cases}\log x & \text{if }0<x\le1,\\0 & \text{if }x>1.\end{cases} $$