Abstract
Denote by M+ the set of probability measures supported on R+. Suppose V-nu is the variance function of the Cauchy-Stieltjes Kernel (CSK) family K-(nu) generated by a non degenerate probability measure nu is an element of 2 M+. We determine the formula for variance function under boolean multiplicative convolution power. This formula is used to identify the relation between variance functions under the map nu (sic) M-t(nu) = (nu(boxed times(t+q)) U1/t+1 from M+ onto itself.