On freely indecomposable measures Hari BercoviciJiun-Chau Wang 46L5430D4030E20free convolutionindecomposable measureanalytic subordinationNevanlinna representation We show that a probability measure is not a nontrivial free convolution if it puts no mass in an interval whose endpoints are atoms. The proof uses analytic subordination. Indiana University Mathematics Journal 2008 text pdf 10.1512/iumj.2008.57.3662 10.1512/iumj.2008.57.3662 en Indiana Univ. Math. J. 57 (2008) 2601 - 2610 state-of-the-art mathematics http://iumj.org/access/