The Dynkin System Generated by the Large Balls of ℝn

Abstract

We prove that in an at least three dimensional Euclidean space the Dynkin system generated by the family of all open balls with radii at least one (that is, the smallest collection containing the open balls with radii at least one and closed under complements and countable disjoint unions) does not contain all Borel sets. We also give a simple characterization of the sets of this Dynkin system.