Geodesic
Local Boundary Behavior of Bounded Holomorphic Functions
Canadian journal of mathematics, Tome 30 (1978) no. 3, pp. 583-592

Voir la notice de l'article provenant de la source Cambridge University Press

Let D ⊂⊂Cn be a bounded domain with smooth boundary ∂D, and let F be a bounded holomorphic function on D. A generalization of the classical theorem of Fatou says that the set E of points on ∂D at which F fails to have nontangential limits satisfies the condition σ (E) = 0, where a denotes surface area measure. We show in the present paper that this result remains true when σ is replaced by 1-dimensional Lebesgue measure on certain smooth curves γ in ∂D. The condition that γ must satisfy is that its tangents avoid certain directions. 
Nagel, Alexander; Rudin, Walter. Local Boundary Behavior of Bounded Holomorphic Functions. Canadian journal of mathematics, Tome 30 (1978) no. 3, pp. 583-592. doi: 10.4153/CJM-1978-051-2
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