Invariant extensions of the Lebesgue measure

Andrzej Hulanicki

Displaying similar documents to “Invariant extensions of the Lebesgue measure”

Some remarks on density points and the uniqueness property for invariant extensions of the Lebesgue measure

A. B. Kharazishvili (1994)

Acta Universitatis Carolinae. Mathematica et Physica

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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

Extensions of invariant measures on Euclidean spaces

Krzysztof Ciesielski, Andrzej Pelc (1985)

Fundamenta Mathematicae

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Some combinatorial problems on the measurability of functions with respect to invariant extensions of the Lebesgue measure

A. B. Kharazishvili (2010)

Acta Universitatis Carolinae. Mathematica et Physica

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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...

On the uniqueness of Lebesgue and Borel measures.

Kharazishvili, A.B. (1997)

Journal of Applied Analysis

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On the generalized Avez method

Antoni Leon Dawidowicz (1992)

Annales Polonici Mathematici

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A generalization of the Avez method of construction of an invariant measure is presented.

On the positivity of an invariant measure on open non-empty sets

Antoni Leon Dawidowicz (1989)

Annales Polonici Mathematici

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Construction of Measure from Semialgebra of Sets1

Noboru Endou (2015)

Formalized Mathematics

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In our previous article [22], we showed complete additivity as a condition for extension of a measure. However, this condition premised the existence of a σ-field and the measure on it. In general, the existence of the measure on σ-field is not obvious. On the other hand, the proof of existence of a measure on a semialgebra is easier than in the case of a σ-field. Therefore, in this article we define a measure (pre-measure) on a semialgebra and extend it to a measure on a σ-field. Furthermore,...