Radial limits and boundary uniqueness

TL;DR

This paper revisits classical theorems in complex analysis related to boundary behavior and radial limits, providing simplified proofs using only traditional methods from Fatou's era.

Contribution

It offers new, simpler proofs of fundamental boundary theorems in complex analysis, relying solely on classical techniques from the early 20th century.

Findings

Simplified proofs of boundary theorems

Use of only classical tools from Fatou's era

Enhanced understanding of boundary behavior in complex analysis

Abstract

The paper sheds a new light on the fundamental theorems of complex analysis due to P. Fatou, F. and M. Riesz, N. N. Lusin, I. I. Privalov, and A. Beurling. Only classical tools available at the times of Fatou are used. The proofs are very simple and in some cases - almost trivial.