H. Simon and B. Szörényi have found an error in the proof of Theorem 52 of “Shifting: One-inclusion mistake bounds and sample compression”, Rubinstein et al. (2009) [3]. In this note we provide a corrected proof of a slightly weakened version of this theorem. Our new bound on the density of one-inclusion hypergraphs is again in terms of the capacity of the multilabel concept class. Simon and Szörényi have recently proved an alternate result in Simon and Szörényi (2009) [4].
