Displaying similar documents to “On the generalized Avez method”

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

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...

Product Pre-Measure

Noboru Endou (2016)

Formalized Mathematics

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In this article we formalize in Mizar [5] product pre-measure on product sets of measurable sets. Although there are some approaches to construct product measure [22], [6], [9], [21], [25], we start it from σ-measure because existence of σ-measure on any semialgebras has been proved in [15]. In this approach, we use some theorems for integrals.

Stretched shadings and a Banach measure that is not scale-invariant

Richard D. Mabry (2010)

Fundamenta Mathematicae

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It is shown that if A ⊂ ℝ has the same constant shade with respect to all Banach measures, then the same is true of any similarity transformation of A and the shade is not changed by the transformation. On the other hand, if A ⊂ ℝ has constant μ-shade with respect to some fixed Banach measure μ, then the same need not be true of a similarity transformation of A with respect to μ. But even if it is, the μ-shade might be changed by the transformation. To prove such a μ exists, a Hamel...

On nonmeasurable selectors of countable group actions

Piotr Zakrzewski (2009)

Fundamenta Mathematicae

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Given a set X, a countable group H acting on it and a σ-finite H-invariant measure m on X, we study conditions which imply that each selector of H-orbits is nonmeasurable with respect to any H-invariant extension of m.