  We establish a so-called counting lemma that allows embeddings of certain
linear uniform hypergraphs into sparse pseudorandom hypergraphs, generalizing a
result for graphs [Embedding graphs with bounded degree in sparse pseudorandom
graphs, Israel J. Math. 139 (2004), 93-137]. Applications of our result are
presented in the companion paper [Counting results for sparse pseudorandom
hypergraphs II].
