Displaying similar documents to “A note on the support of right invariant measures.”

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...

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...

Invariant extension of Haar measure

Antal Járai

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CONTENTS§1. Introduction...............................................................5§2. Covariant extension of measures..............................6§3. An invariant extension of Haar measure..................15§4. Covariant extension of Lebesgue measure.............22References....................................................................26