Abstract:
The aim of this thesis is to study Szemeredi’s Regularity Lemma from an analytical point of view. We are going to explain how one can interpret the so-called Szemeredi’s Regularity Lemma in the language of analysis. By using this language, we are going to prove two analytical statements which imply several (both analytical and graph theoretical) forms of Szemeredi’s Regularity Lemma. For the sake of completeness, we will present a combinatorial proof of the standard form of this lemma in the appendix.
