On Minkowski sums of many small sets (Q1755986)

A subset of a normed space is said to be infinitely divisible if it can be represented as the Minkowski sum of finitely many sets of arbitrarily small diameters. The main result of this paper is: Theorem 1. A weakly closed set in a Banach space is infinitely divisible if and only if it is convex and bounded. While one implication is obvious, the other is proved reducing it to the case of \(\mathbb{R}^d\).