Abstract
Suppose V-nu is the pseudo-variance function of the Cauchy-Stieltjes Kernel family K-(nu) generated by a non degenerate probability measure nu on the positive real line. We determine explicitly the law of large numbers mu for free multiplicative convolution given by Haagerup and Moller in terms of the pseudo-variance function V-nu. Some examples of calculations of mu are given for probability measures nu of importance in free probability.