prove the convexity of zero one loss multiple a convex function I am now working on a problem To prove the convexity of a zero-one loss multiple with a convex function, and it looks like this: $$L(s) = s^2 \times \boldsymbol 1(s\leq 0);$$ when proving this convexity, is it ok to assume this $\boldsymbol 1(s\leq 0)$ a constant?
if it is not ok to treat 1(s<=0) as constant, how would we prove the convexity then?

This $\boldsymbol 1(s\leq 0)$, is not a constant.  It has the value
$$\boldsymbol 1(s\leq 0) =\begin{cases} 1 & \text{if $s\leq0$} \\ 0 & \text{if $s>0$}\end{cases}$$
and the product
$$s^2 \times \boldsymbol 1(s\leq 0) =\begin{cases} s^2 & \text{if $s\leq0$} \\ 0& \text{if $s>0$}\end{cases}$$
