On nonmeasurable selectors of countable group actions

Zakrzewski, Piotr

doi:10.4064/fm202-3-5

Fund. Math.

2009

DOI: 10.4064/fm202-3-5

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On nonmeasurable selectors of countable group actions

Piotr Zakrzewski

Abstract: Abstract. 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.

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Cited by 2 publications

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On Countable Almost Invariant Partitions of G-Spaces

Kharazishvili¹

2014

Ukr Math J

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For any σ-finite G-quasiinvariant measure µ given in a G-space which is G-ergodic and possesses the Steinhaus property, it is shown that every nontrivial countable µ-almost G-invariant partition of the G-space has a µ-nonmeasurable member. Для будь-якoї σ-скiнченної G-квазiiнварiантної мiри µ, що задана на G-просторi, є G-ергодичною та має властивiсть Штейнхауса, показано, що кожне нетривiальне розбиття µ-майже G-iнварiантного розбиття G-простору має µневимiрний член.

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On Countable Almost Invariant Partitions of G-Spaces

Kharazishvili¹

2014

Ukr Math J

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Nonmeasurable Vitali set: variations on theme

Bella

Puglisi

Villani

2022

Quaestiones Mathematicae

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On nonmeasurable selectors of countable group actions

Abstract: Abstract. 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.

Cited by 2 publications

References 11 publications

On Countable Almost Invariant Partitions of G-Spaces

On Countable Almost Invariant Partitions of G-Spaces

Nonmeasurable Vitali set: variations on theme

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