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Covering the Plane with Denumerably Many CurvesJournal of The London Mathematical Society-second Series
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Kharazishvili (1994)
SOME QUESTIONS CONCERNING INVARIANT EXTENSIONS OF LEBESGUE MEASUREReal analysis exchange, 20
The notions of a negligible set and of an absolutely nonmeasurable set are introduced and discussed in connection with the measure extension problem. In particular, it is demonstrated that there exist subsets of the plane 𝐑 2 which are 𝑇 2 -negligible and, simultaneously, 𝐺-absolutely nonmeasurable. Here 𝑇 2 denotes the group of all translations of 𝐑 2 and 𝐺 denotes the group generated by {𝑔} ∪ 𝑇 2 , where 𝑔 is an arbitrary rotation of 𝐑 2 distinct from the identity transformation and all central symmetries of 𝐑 2 .
Georgian Mathematical Journal – de Gruyter
Published: Sep 1, 2004
Keywords: Sierpiński partition; quasi-invariant measure; uniform set; negligible set; absolutely nonmeasurable set
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