On a boundary property of Blaschke products

TL;DR

This paper characterizes the boundary behavior of Blaschke products, showing that they lack radial limits on certain measure-zero sets while having unrestricted limits elsewhere, based on the set being closed.

Contribution

It provides a precise boundary property criterion for Blaschke products related to measure-zero and closed sets on the unit circle.

Findings

Blaschke products lack radial limits on measure-zero sets.

They have unrestricted limits outside these sets.

The boundary property is characterized by the set being closed of measure zero.

Abstract

A Blaschke product has no radial limits on a subset $E$ of the unit circle $T$ but has unrestricted limit at each point of $T \setminus E$ if and only if $E$ is a closed set of measure zero.