Absolute continuity of autophage measures on finite-dimensional vector spaces

Abstract

We consider a class of measures called autophage which was introduced and studied by Szekely for measures on the real line. We show that the autophage measures on finite-dimensional vector spaces over real or Qp are infinitely divisible without nontrivial idempotent factors and are absolutely continuous with bounded continuous density. We also show that certain semistable measures on such vector spaces are absolutely continuous. (© 2004 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)