Gaussian Random Functions - M. A. Lifshits.
Barcelona Seminar on Stochastic Analysis - D. Nualart; M. Sanz-Solé.
Permutations preserving Cesàro mean, densities of natural numbers and uniform distribution of sequences
We are interested in permutations preserving certain distribution properties of sequences. In particular we consider -uniformly distributed sequences on a compact metric space , 0-1 sequences with densities, and Cesàro summable bounded sequences. It is shown that the maximal subgroups, respectively subsemigroups, of leaving any of the above spaces invariant coincide. A subgroup of these permutation groups, which can be determined explicitly, is the Lévy group . We show that is big in the...
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