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Shift invariant measures and simple spectrum. (English) Zbl 0965.60003

Summary: We consider some descriptive properties of supports of shift invariant measures on \(\mathbb{C}^\mathbb{Z}\) under the assumption that the closed linear span (in \(L^2)\) of the coordinate functions on \(\mathbb{C}^\mathbb{Z}\) is all of \(L^2\).

MSC:

60A05 Axioms; other general questions in probability
47A35 Ergodic theory of linear operators
28D05 Measure-preserving transformations
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