  Szemer\'edi's regularity lemma is a basic tool in graph theory, and also
plays an important role in additive combinatorics, most notably in proving
Szemer\'edi'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 variant of this lemma which introduces a new
parameter $F$. This stronger version of the regularity lemma was iterated in a
recent paper of the author to reprove the analogous regularity lemma for
hypergraphs.
