Kurt Gödel Research Center

2014 seminar talk: Definability of Pure Unrectifiability

Talk held by Vadim Kulikov (KGRC) at the KGRC seminar on 2014-04-03.

Abstract

We will look at various notions which arise in geometric measure theory such as "positive Hausdorff-measure" and "purely unrectifiable" (a subset of a Hilbert space is purely unrectifiable if its intersection with any smooth curve has 1-dimensional Hausdorff measure zero). Some open questions in geometric measure theory reside around characterizing these properties in various ways. Here I present a result which might contribute to that program, namely proving descriptive set theoretic complexities of these classes of sets.