Kurt Gödel Research Center

2018 seminar talk: Combinatorial variants of Lebesgue's density theorem

Talk held by Philipp Schlicht (Universität Bonn, Germany) at the KGRC seminar on 2018-01-18.

Abstract

We introduce density points relative to an arbitrary sigma-ideal of Borel subsets of the Cantor or Baire space, and define the density property relative to a sigma-ideal as a variant of Lebesgue’s density property. For the ideal of null sets with respect to the uniform measure on the Cantor space, our density points coincide with the standard definition up to a null set. The main results show that many well-known ccc ideals have the density property and that this fails for many non-ccc ideals. In the talk, I will present the current status of this project.

This is joint work with Sandra Müller, David Schrittesser and Thilo Weinert.