Displaying similar documents to “The Minlos lemma for positive-definite functions on additive subgroups of ℝ n ”

On concentrated probabilities

Wojciech Bartoszek (1995)

Annales Polonici Mathematici

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Let G be a locally compact Polish group with an invariant metric. We provide sufficient and necessary conditions for the existence of a compact set A ⊆ G and a sequence g n ∈ G such that μ ∗ n ( g n A ) ≡ 1 for all n. It is noticed that such measures μ form a meager subset of all probabilities on G in the weak measure topology. If for some k the convolution power μ ∗ k has nontrivial absolutely continuous component then a similar characterization is obtained for any locally compact, σ-compact, unimodular, Hausdorff...

Conical measures and vector measures

Igor Kluvánek (1977)

Annales de l'institut Fourier

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Every conical measure on a weak complete space E is represented as integration with respect to a σ -additive measure on the cylindrical σ -algebra in E . The connection between conical measures on E and E -valued measures gives then some sufficient conditions for the representing measure to be finite.

A property of Fourier Stieltjes transforms on the discrete group of real numbers

Yngve Domar (1970)

Annales de l'institut Fourier

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Let μ be a Fourier-Stieltjes transform, defined on the discrete real line and such that the corresponding measure on the dual group vanishes on the set of characters, continuous on R . Then for every ϵ > 0 , { x ∈ R | Re ( μ ( x ) ) > ϵ } has a vanishing interior Lebesgue measure. If ϵ = 0 the statement is not generally true. The result is applied to prove a theorem of Rosenthal.

On continuous collections of measures

Robert M. Blumenthal, Harry H. Corson (1970)

Annales de l'institut Fourier

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An integral representation theorem is proved. Each continuous function from a totally disconnected compact space M to the probability measures on a complete metric space X ‾ is shown to be the resolvent of a probability measure on the space of continuous functions from M to X ‾ .