On concentrated probabilities

Wojciech Bartoszek

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On concentrated probabilities on non locally compact groups

Wojciech Bartoszek (1996)

Commentationes Mathematicae Universitatis Carolinae

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Let $G$ be a Polish group with an invariant metric. We characterize those probability measures $μ$ on $G$ so that there exist a sequence $g_{n} \in G$ and a compact set $A \subseteq G$ with $μ^{* n} (g_{n} A) \equiv 1$ for all $n$ .

The uniqueness of Haar measure and set theory

Piotr Zakrzewski (1997)

Colloquium Mathematicae

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Let G be a group of homeomorphisms of a nondiscrete, locally compact, σ-compact topological space X and suppose that a Haar measure on X exists: a regular Borel measure μ, positive on nonempty open sets, finite on compact sets and invariant under the homeomorphisms from G. Under some mild assumptions on G and X we prove that the measure completion of μ is the unique, up to a constant factor, nonzero, σ-finite, G-invariant measure defined on its domain iff μ is ergodic and the G-orbits...

The convolution equation $P = P^{*} Q$ of Choquet and Deny and relatively invariant measures on semigroups

Arunava Mukherjea (1971)

Annales de l'institut Fourier

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Choquet and Deny considered on an abelian locally compact topological group the representation of a measure $P$ as the convolution product of itself and a finite measure $Q : P = P^{*} Q$ . In this paper, we make an attempt to find, in the case of certain locally compact semigroups, those solutions $P$ of the above equation which are relatively invariant on the support of $Q$ . A characterization of relatively invariant measures on certain locally compact semigroups is also presented. Our results...

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 $\overline{X}$ is shown to be the resolvent of a probability measure on the space of continuous functions from $M$ to $\overline{X}$ .

Reciprocities on groups

Artiaga, Lucio, Takahashi, Shuichi (1972)

Portugaliae mathematica

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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.

Displaying similar documents to “On concentrated probabilities”