Geodesic
A Problem of Gelfand on Rings of Operators and Dynamical Systems
Canadian journal of mathematics, Tome 22 (1970) no. 3, pp. 514-517

Voir la notice de l'article provenant de la source Cambridge University Press

Let G be a separable locally compact group (separable in the sense that the topology of G has a countable base). Let S be a standard Borel space on which G acts on the right such that:(1) s · g 1 g 2 = (s · g 1) · g 2;(2) s · e = s;(3) (s, g) → s · g is a Borel function from S × G to S.If μ is a Borel measure on S, let μg be the Borel measure on S defined by μg(E) = μ(E · g).Let μ be a Borel measure on S which is quasi-invariant under the action of G; i.e., μg and μ are absolutely continuous (g ∈ G). The triple (G, S, μ) is called a dynamical system [11; 8].Consider the following general problem. Let (G, S, μ) be a dynamical system. 
Kallman, Robert R. A Problem of Gelfand on Rings of Operators and Dynamical Systems. Canadian journal of mathematics, Tome 22 (1970) no. 3, pp. 514-517. doi: 10.4153/CJM-1970-058-x
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