Non-tangential and probabilistic boundary behavior of pluriharmonic functions
نویسنده
چکیده
Let u be a pluriharmonic function on the unit ball in Cn. I consider the relationship between the set of points Lu on the boundary of the ball at which u converges non-tangentially, and the set of points Lu at which u converges along conditioned Brownian paths. For harmonic funcitons u of two variables, the result Lu a.e. = Lu has been known for some time, as has a counterexample to the same equality for three variable harmonic functions. I extend the Lu a.e. = Lu result to pluriharmonic functions in arbitrary dimensions.
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