Let X be a locally convex Hausdorff space, K - its compact, convex and metrizable subset. We say, that a regular Borel probability measure μ on K represents point x;ϵX if the equality f(x) = ∫fdμ holds for every f ϵ X*. We will show by a simple example, that the set of such measures supported on ext K need not be closed.
Using the winding of measures on torus in “rational directions” special classes of unitary operators and pairs of isometries are defined. This provides nontrivial examples of generalized powers. Operators related to winding Szegö-singular measures are shown to have specific properties of their invariant subspaces.
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