Baire Category Lower Density Operators with Borel Values

TL;DR

This paper investigates the properties of lower density operators related to Baire category points in the real line and Cantor space, showing they have Borel values of a specific complexity class, extending measure-theoretic analogies.

Contribution

It introduces the notion of Baire category density points in the Cantor space and proves their associated lower density operators have Borel values of class pi^0_3, similar to the measure case.

Findings

Lower density operator for Baire category points has pi^0_3 Borel values.

Baire category density points in Cantor space generate similar lower density operators.

Results extend measure-theoretic concepts to Baire category context.

Abstract

We prove that the lower density operator associated with the Baire category density points in the real line has Borel values of class $\pmb \Pi^0_3$ which is analogous to the measure case. We also introduce the notion of the Baire category density point of a subset with the Baire property of the Cantor space, and we prove that it generates a lower density operator with Borel values of class $\pmb \Pi^0_3$.