The non-covered set in Dvoretzky covering is a set of multiplicity

TL;DR

This paper proves that in Dvoretzky's random covering, the non-covered set has a multiplicity property by demonstrating that the associated multiplicative chaotic measure is a Rajchman measure.

Contribution

It establishes that the non-covered set in Dvoretzky covering is of multiplicity through the analysis of the chaotic measure's properties.

Findings

The non-covered set has a multiplicity property.

The multiplicative chaotic measure is a Rajchman measure.

Provides insight into the structure of non-covered sets in random coverings.

Abstract

We prove that the non-covered set in Dvortezky random covering is a set of multiplicity, by showing that the natural multiplicative chaotic measure is a Rajchman measure.