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A method of construction of an invariant measure. (English) Zbl 0784.28004

Let \(V\) denote the space of all Lipschitz functions on [0,1] vanishing at 0. For \(v\in V\), \(t\geq 0\) and \(\lambda>1\) put \(T_ tv(x)=e^{\lambda t}v(xe^{-t})\). The author presents a sufficient condition allowing to construct an invariant measure for this semidynamical system (it is unique).

MSC:

28C10 Set functions and measures on topological groups or semigroups, Haar measures, invariant measures
28D05 Measure-preserving transformations
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