Sublacunary sequences that are strong sweeping out.

An increasing sequence (an) of positive integers which satisfies an+1/an ≥ 1+ŋ for some positive ŋ is called a lacunary sequence. It has been known for over twenty years that every lacunary sequence has the strong sweeping out property which means that in every aperiodic dynamical sys¬tem we can find a set E of arbitrary small measure so that ... and ... almost everywhere. In this paper, we improve this result by showing that if (an) satisfies only ... for some positive ŋ,, then it already has the strong sweeping out property. [ABSTRACT FROM AUTHOR]