For a Banach space $X$ we demonstrate the equivalence of the following two properties: (1) $X$ is B-convex (that is, possesses a nontrivial infratype), and (2) if ${ F: [0,1] \to 2^{ X} \setminus \{ \varnothing\}}$ is a { multifunction}, $\mathrm{ conv} F$ denotes the mapping $t \mapsto \mathrm{ conv} F(t)$, then the Riemann integrability of $\mathrm{ conv} F$ is equivalent to the Riemann integrability of $F$. For multifunctions with compact values the Riemann integrability of $\mathrm{ conv} F$ is equivalent to the Riemann integrability of $F$ without any restrictions on the Banach space $X$.
Categories: math.FA