On semiregular points of the Martin boundary
Aurel Cornea, Peter A. Loeb · Proceedings of the American Mathematical Society · 1988
For a selfadjoint, Brelot harmonic space with Martin boundary, call "semiregular" a point z z of the boundary at which the Green function has a positive upper limit; call "maximal" the filter F z {\mathcal {F}_z} converging to z z along which that upper limit is attained. If such a z z is minimal then any bounded harmonic function has a limit along F z {\mathcal {F}_z} and F z {\mathcal {F}_z} is coarser than the fine filter associated with z z . The semiregular points form a set of harmonic measure zero.