Let $f_{1},\dots,f_{l}$ be concave functions.

1. (1)

   If $\operatorname{stab}(f_{1})\cap\dots\cap\operatorname{stab}(f_{l})\not=\emptyset$, then

   $$(f_{1}\boxplus\dots\boxplus f_{l})^{\vee}=f_{1}^{\vee}+\dots+f_{l}^{\vee}.$$

2. (2)

   If ${\operatorname{dom}}(f_{1})\cap\dots\cap{\operatorname{dom}}(f_{l})\not=\emptyset$, then

   $$({\operatorname{cl}}(f_{1})+\dots+{\operatorname{cl}}(f_{l}))^{\vee}={\operatorname{cl}}(f_{1}^{\vee}\boxplus\dots\boxplus f_{l}^{\vee}).$$

3. (3)

   If $\operatorname{ri}({\operatorname{dom}}(f_{1}))\cap\dots\cap\operatorname{ri}({\operatorname{dom}}(f_{l}))\not=\emptyset$, then

   $$(f_{1}+\dots+f_{l})^{\vee}=f_{1}^{\vee}\boxplus\dots\boxplus f_{l}^{\vee}.$$