In my research I use a definition of convex hull that is compatible with measure theory, in the sense that it ignores negligible sets.
Are there any references to the following concept, or similar concepts, in the literature? (The name, obviously, need not be the same.)
Suppose $A \subset \mathbb{R}^d$, $d \in \mathbb{Z}_+$. Define the closed essential convex hull of $A$ as the intersection of all half-spaces $H \subset \mathbb{R}^d$ that satisfy \begin{equation} m(A \setminus H) = 0, \end{equation} where $m$ is the $d$-dimensional Lebesgue measure.
We were unable to find anything in the literature, so now some basic facts can be found in the preprint https://arxiv.org/abs/1703.02814 .