Abstract. Let G be a countable amenable group containing subgroups of arbitrarily large finite index. Given a polyhedron P and a real number ρ such that 0 ≤ ρ ≤ dim(P ), we construct a closed subshift X ⊂ P G having mean topological dimension ρ. This shows in particular that mean topological dimension of compact metrisable G-spaces take all values in [0, ∞].
Let G be a countable amenable group and P a polyhedron. The mean topological dimension mdim(X, G) of a subshift X ⊂ P G is a real number satisfying 0 ≤ mdim(X, G) ≤ dim(P ), where dim(P ) denotes the usual topological dimension of P . We give a construction of minimal subshifts X ⊂ P G with mean topological dimension arbitrarily close to dim(P ).
Dédié à Anatole Katok pour son 60 ème anniversaire RÉSUMÉ. Dans cette note on démontre un théorème de convergence pour les fonctions sous-additives invariantes définies sur les parties finies d'un groupe dénombrable moyennable. Ce théorème peut être déduit d'un résultat général dû à D. S. Ornstein et B. Weiss. La démonstration que l'on présente ici suit une preuve esquissée par M. Gromov.
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