Abstract. Szemerédi’s regularity lemma is a basic tool in graph theory, and also plays an important role in additive combinatorics, most notably in proving Szemerédi’s theorem on arithmetic progressions , . In this note we revisit this lemma from the perspective of probability theory and information theory instead of graph theory, and observe a slightly stronger variant of this lemma, related to similar strengthenings of that lemma in . This stronger version of the regularity lemma was extended in  to reprove the analogous regularity lemma for hypergraphs. 1.