The topics include Brownian motion and

harmonic measure in conic sections, the sharpness of certain approach regions, integral representation for space-time excessive functions, hyperbolic Riemann surfaces without unbounded positive harmonic functions, and a vanishing theorem on the point- wise defect of a rational iteration sequence for moving targets.

For example, consider D = {[z.sub.0]} [subset] G and [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII], the so-called harmonic measure of [z.sub.0].

where [w.sub.z] denotes the harmonic measure. Since D is compact, the latter implies that

This is the well-known characterization of the harmonic measure [rho] = [[omega].sub.z] by the mean-value principle.

The paper is organized into four sections: in the first the number of branches of [gamma] \ [gamma] is counted; in the second the theorem on proper maps is proved; in the third Stokes's theorem is proved; we end the paper with a discussion of density at the boundary and harmonic measure on [gamma].

The usefulness of this construction lies in the fact that harmonic measure on [[omega].sub.1] is not singular to harmonic measure on [[omega].sub.2].

Density at the boundary and harmonic measure. We obtain here a partial result about the two dimensional density at the boundary of [gamma]; we end the chapter with a brief discussion of the problem of harmonic measure on [gamma].

Harmonic measure; geometric and analytic points of view.