Abstract
We provide examples of a nested sequences of sets {S_n}, suitably sparse, residing in a group G, for which multidimensional averages fail converge pointwise for f in certain L^p spaces, but do converge in others, for any free group action T. Our construction involves the method of perturbation pioneered by A. Bellow and applied in the integer cases by K. Reinhold and M. Wierdl.
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