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Uniformly cyclic vectors

Joseph Rosenblatt (2006)

Colloquium Mathematicae

A group acting on a measure space (X,β,λ) may or may not admit a cyclic vector in L ( X ) . This can occur when the acting group is as big as the group of all measure-preserving transformations. But it does not occur, even though there is no cardinality obstruction to it, for the regular action of a group on itself. The connection of cyclic vectors to the uniqueness of invariant means is also discussed.

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