Let $X$ a Banach space and $A \subset X$ a subset. I know the notation $\text{conv}(A)$ denotes the convex hull of $A$. What means the notation $\overline{\text{conv}}(A)$ used in comments in this discussion? My (naive) guess: one takes the intersection only over all closed convex subsets containing $A$. Is it correct?
I saw here that it is considered as the closure of the convex hull. But wouldn't in that case the notation $\overline{\text{conv}(A)}$ syntactically more meaningful? This lead me to conjecture that the notation $\overline{\text{conv}}(A)$ should mean something different by definition.