Abstract
LetX andY be finite sets and, for eachnεN,f n :X→Y. If λ and μ are probability measures onX andY resp., we ask the following question: How has the sequence (f n ) nεN to look like such that every sequence (x n ) nεN with distribution λ induces a sequence (f n (x n )) nεN with distribution μ? A satisfactory description of these so called (λ,μ)-uniform distribution preserving sequences of maps is the object of this paper. Almost constant sequences and related notions are the key for an adequate understanding of the problem.
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Dedicated to Prof. Hlawka on the occasion of his 80th birthday
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Winkler, R. Distribution preserving sequences of maps and almost constant sequences on finite sets. Monatshefte für Mathematik 126, 161–174 (1998). https://doi.org/10.1007/BF01473584
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DOI: https://doi.org/10.1007/BF01473584