Abstract
In this paper we answer a question of J. Bourgain which was motivated by questions A. Bellow and H. Furstenberg. We show that the sequencefn 2 g 1D1 is L 1 -universally bad. This implies that it is not true that given a dynamical system .X;U;;T/ andf 2L 1 ./ , the ergodic means
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