MathDB
borel sets

Source: miklos schweitzer 2011 q1

August 29, 2021
Measure theorytopology

Problem Statement

Let F1,F2,...F_1, F_2, ... be Borel-measurable sets on the plane whose union is the whole plane. Prove that there is a natural number n and circle S for which the set SFnS \cap F_n is dense in S. Also show that the statement is not necessarily true if we omit the condition for the measurability of sets FjF_j.