Abstract

Abstract. Recent work of Gowers [10] and Nagle, Rödl, Schacht, and Skokan [15], [19], [20] has established a hypergraph removal lemma, which in turn implies some results of Szemerédi [26] and Furstenberg-Katznelson [7] 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 [29] to establish (among other things) infinitely many constellations of a prescribed shape in the Gaussian primes. 1.

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