Harmonic measure in convex domains

Let Q be an open, convex subset of R^. At almost every point x of dQ, with respect to surface measure da, there is a unique outer unit normal 6. The map g: dQ -* S n given by g (x) = 9 and defined almost everywhere is called the Gauss map. (S n, n = N -1, is the unit sphere in R^. ) Suppose that the origin 0 belongs to Q. Harmonic measure for fit at 0 is the probability measure co such that for all continuous functions on dQ 1, M (0) = f fdco Jan where u solves the Dirichlet problem: Au = 0 in Q and u = on dQ.