A characterization of certain compact sets of measure zero

Abstract

AbstractWe show that the only compact subsets of [0, 1] of measure zero are the obvious ones, and extend this idea to show that the only compact subsets of [0, 1] that generate semigroups of ℝ of measure zero are the obvious ones. We apply this last result to prove that any proper Raikov system of subsets of ℝ, with a single generator, is contained in a strictly larger proper Raikov system.