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Permutations preserving Cesàro mean, densities of natural numbers and uniform distribution of sequences

M. BlümlingerN. Obata — 1991

Annales de l'institut Fourier

We are interested in permutations preserving certain distribution properties of sequences. In particular we consider μ -uniformly distributed sequences on a compact metric space X , 0-1 sequences with densities, and Cesàro summable bounded sequences. It is shown that the maximal subgroups, respectively subsemigroups, of A u t ( N ) leaving any of the above spaces invariant coincide. A subgroup of these permutation groups, which can be determined explicitly, is the Lévy group 𝒢 . We show that 𝒢 is big in the...

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