%0 Journal Article %T On regularity for measures in multiplicative free convolution semigroups %A Ping Zhong %J Mathematics %D 2011 %I arXiv %X Given a probability measure $\mu$ on the real line, there exists a semigroup $\mu_t$ with real parameter $t>1$ which interpolates the discrete semigroup of measures $\mu_n$ obtained by iterating its free convolution. It was shown in \cite{[BB2004]} that it is impossible that $\mu_t$ has no mass in an interval whose endpoints are atoms. We extend this result to semigroups related to multiplicative free convolution. The proofs use subordination results. %U http://arxiv.org/abs/1112.2783v2