On regular points of the Martin boundary

We introduce the conception of a weakly regular point of the Martin boundary and prove that almost all the points of the Martin boundary (with respect to the harmonic measure) are weakly regular for a wide class of self-adjoint Markov processes (theorem 2). If a process of this class is continuous and its Martin boundary is at most countable, almost all its points are regular in the strict sense (theorem 3). We give an example which shows that a weakly regular point may be irregular.