On the positivity of an invariant measure on open non-empty sets
Antoni Leon Dawidowicz (1989)
Annales Polonici Mathematici
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Antoni Leon Dawidowicz (1989)
Annales Polonici Mathematici
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A. B. Kharazishvili (1994)
Acta Universitatis Carolinae. Mathematica et Physica
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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
Antoni Leon Dawidowicz (1992)
Annales Polonici Mathematici
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A method of construction of an invariant measure on a function space is presented.
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...
A. B. Kharazishvili (2010)
Acta Universitatis Carolinae. Mathematica et Physica
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Paweł Góra (1989)
Banach Center Publications
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Andrzej Hulanicki (1962)
Fundamenta Mathematicae
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A. B. Kharazishvili (2008)
Acta Universitatis Carolinae. Mathematica et Physica
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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.
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...
Kharazishvili, A.B. (1997)
Journal of Applied Analysis
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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.