Abstract

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 nontangentially and the set of points ℒu at which u converges along conditioned Brownian paths. For harmonic functions u of two variables, the result $L_{u}\stackrel{\mathrm{a.e.}}{=}\mathscr{L}_{u}$ has been known for some time, as has a counterexample to the same equality for three variable harmonic functions. I extend the $L_{u}\stackrel{\mathrm{a.e.}}{=}\mathscr{L}_{u}$ result to pluriharmonic functions in arbitrary dimensions.

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