The Elek-Szegedy Proof of Szemeredi's Theorem, II

I will introduce nonstandard analysis, and show that the existence of a separable realization (a type of map between nonstandard measures and Lebesgue measure) implies the simplex removal lemma. This portion of the proof, which uses a mix of nonstandard and classical measure theory, is the conceptual heart of the entire argument. In a subsequent talk, I will engage the technically challenging issue of proving that a separable realization exists.

Kevin O'Bryant