2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/101157Recent work of Gowers and Nagle, Rödl, Schacht, and Skokan has established a hypergraph removal lemma, which in turn implies some results of Szemerédi and Furstenberg-Katznelson concerning one-dimensional and multi-dimensional arithmetic progressions respectively. In this paper we shall give a self-contained proof of this hypergraph removal lemma. In fact we prove a slight strengthening of the result, which we will use in a subsequent paper to establish infinitely many constellations of a prescribed shape in the Gaussian primes.25 pages, no figures, to appear, J. Combin. Thy A. This is the final version, incorporating the referee's commentsCombinatorics05C65text