For each $i=1,\dots,l$, let $f_{i}$ be a concave function and $\lambda_{i}>0$ a real number. Then

1. (1)

   $\partial\left(\sum_{i}\lambda_{i}f_{i}\right)\supset\sum_{i}\lambda_{i}\partial(f_{i})$;

2. (2)

   if $\operatorname{ri}({\operatorname{dom}}(f_{1}))\cap\dots\cap\operatorname{ri}({\operatorname{dom}}(f_{l}))\neq\emptyset$, then

   (3.44)

   $$\partial\bigg(\sum_{i}\lambda_{i}f_{i}\bigg)=\sum_{i}\lambda_{i}\partial(f_{i}).$$