On Lebesgue Measure of Integral Self-Affine Sets

Let A be an expanding integer n x n matrix and D be a finite subset of Z(n). The self-affine set T = T (A, D) is the unique compact set satisfying the equality A(T) = boolean OR(d is an element of D) (T + d). We present an effective algorithm to compute the Lebesgue measure of the self-affine set T, the measure of the intersection T boolean AND (T + u) for u is an element of Z(n), and the measure of the intersection of self-affine sets T (A, D(1)) boolean AND T (A, D(2)) for different sets D(1), D(2) is an element of Z(n).