Regularity lemmas in a Banach space setting

摘要

Szemeredi's regularity lemma is a fundamental tool in extremal graph theory, theoretical computer science and combinatorial number theory. Lovasz and Szegedy (2007) gave a Hilbert space interpretation of the lemma and an interpretation in terms of compactness of the space of graph limits. In this paper we prove several compactness results in a Banach space setting, generalising results of Lovasz and Szegedy (2007) as well as a result of Borgs et al. (2014). (C) 2015 Elsevier Ltd. All rights reserved.