Logic Seminar

We show that a closed disk and square with the same area are equidecomposible with Gδ pieces. A simple argument implies that the pieces are also Fσ. Indeed the argument takes advantage of closure properties of the class of sets that are both Gδ and Fσ. More generally, we show that if A and B have the same positive Lebesgue measure and small boundary, then they are equidecomposible with pieces that are countable unions of finite Boolean combinations of translates of A, B and open sets. This is joint work with Narmada Varadarajan and Felix Weilacher.