We will show a counterintuitive combinatorial property of all positive planar measures which seemingly goes against a known counterexample of Carleson of a quilt of an arbitrary small measure. Of course our property does not contradict Carleson's example, and we will show relations between these two. This is a joint work with Pavel Mozolyako, Pavel Zorin-Kranich and Nicola Arcozzi. Speaker(s): Alexander Volberg (Michigan State University)