Mathematical Institute of Slovak Academy of Sciences, Jesenná~5, 04154 Kosice, Slovakia
Abstract:
We introduce the notion of perfectly measure zero sets and prove that every perfectly measure zero set is permitted for the families of all pseudo-Dirichlet sets, N-sets, A-sets and N-sets. In particular this means that these families of trigonometric thin sets are closed under adding sets of cardinality less than the additivity of Lebesgue measure.