A note on functions regular and bounded in the unit circle and small at a set of points near the circumference of the circle
B. J. Maitland · Mathematical Proceedings of the Cambridge Philosophical Society · 1939
The following theorem was proved by Milloux: Theorem A. Suppose that f (z) is regular and that | f(z) | < 1 in the unit circle. Suppose also that the set of points in the circle | z | ≤ r′ < 1 at which cannot be enclosed in circles, the sum of whose radii is equal to 2eh−1. Then where K is a numerical constant.