Rauzy, Gérard Ensembles à restes bornés. (English) Zbl 0547.10044 Sémin. Théor. Nombres, Univ. Bordeaux I 1983-1984, Exp. No. 24, 12 p. (1984). Let X be a topological space, \(u=(u_ n)\), \(n\in {\mathbb{N}}\) a sequence with elements in X. The author investigates subsets \(A\subseteq X\) with the following property: There exist a,C (real numbers): such that for all \(N\in {\mathbb{N}} | card\{n<N, u_ n\in A\}-Na|\leq C.\) The author establishes several results concerning such subsets A and sequences \(u_ n=T^ nx_ 0\), where T denotes a certain transformation on X (e.g. \(X={\mathbb{R}}/{\mathbb{Z}}\), \(Tx=x+\alpha mod 1\), \(\alpha\) irrational). Reviewer: R.F.Tichy Cited in 2 ReviewsCited in 19 Documents MSC: 11K06 General theory of distribution modulo \(1\) Keywords:uniform distribution in abstract spaces; topological space PDFBibTeX XML Full Text: EuDML