Alessandro Andretta: Some descriptive set theory related to the Lebesgue density theorem

Week 2, Monday June 22, 09:00-09:50

The Lebesgue density theorem says that if A (a subset of 2^omega) is measurable, then A is almost equal to D(A), the points of 2^omega where A has density 1. Therefore D selects a set from each measure class. It turns out that D(A) Pi^0_3 --- in fact it can be complete Pi^0_3. I will present some partial results on the complexity of D(A) for various sets A.
This is joint work with Riccardo Camerlo.