weak star density of atomic invariant measures ? - MathOverflow most recent 30 from http://mathoverflow.net 2013-06-20T02:33:58Z http://mathoverflow.net/feeds/question/85319 http://www.creativecommons.org/licenses/by-nc/2.5/rdf http://mathoverflow.net/questions/85319/weak-star-density-of-atomic-invariant-measures weak star density of atomic invariant measures ? IJ 2012-01-10T07:52:53Z 2012-01-10T07:56:31Z <p>Let us consider expanding maps \$E_m: x\mapsto mx\$ on the circle written additively. If we consider the set of all \$E_2\$ invariant probability Borel measures then the convex hull of atomic measures generated by \$E_2\$ periodic points are weak star dense in this set. </p> <p>I want to ask whether this is true for the set of probability Borel measures invariant under both maps \$E_2\$ and \$E_3.\$ </p>