Covariance matrices of self-affine measures

In this paper we derive a formula for the covariance matrix of any self-affine measure, i.e.a probability measure [mu] satisfying where is a family of affine contractive maps and {pk}1<=k<=l is a set of probability weights. In particular if for every k, Ak=A then the formula has the following form where D2X denotes the covariance matrix of the measure [mu] and denotes a covariance matrix of a discrete random variable with values , and corresponding probabilities pk.