Thin Sets at the Boundary
Hiroaki Aikawa · Proceedings of the London Mathematical Society · 1992
In his letter [18], Hayman raised the following questions: If u is negative subharmonic in the unit disk, then for almost all ϕ, u(z) has a limit as z tends to eiϕ nontangentially and outside a near-thin set ([17, Chapter 7]). There ought to be a global result, i.e. not in an angle, outside a suitable exceptional set. What should it be? It might be easier