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Permutations des entiers et répartition des suites. (Permutations of integers and distribution of sequences). (French) Zbl 0581.10026
The permutations h of the positive integers which transform every $$\mu$$- distributed (resp. $$\mu$$-well distributed) sequence u with values in a compact metric space X into a sequence $$u\circ h$$ which is $$\mu$$- distributed (resp. $$\mu$$-well distributed) too, are studied. Some extensions of results of H. Rindler [Acta Arith. 35, 189-193 (1979; Zbl 0335.10051) and Arch. Math. 32, 185-199 (1979; Zbl 0409.10036)] are obtained. (A sequence $$u=(x_ n)$$ with elements in X is called $$\mu$$- distributed to the normalized Borel measure $$\mu$$ if $(*)\quad \lim_{N\to \infty}(1/N)\sum^{N}_{k=1}f(x_ n)=\int_{X}f d\mu$ for all continuous real-valued functions f on X; $$(x_ n)$$ is $$\mu$$-well distributed if $$(x_{n+m})$$ satisfies (*) uniformly in $$m=0,1,2,...)$$.
Reviewer: R.F.Tichy

##### MSC:
 11K06 General theory of distribution modulo $$1$$