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- W2463762018 abstract "It is introduced a certain approach for equipment of sets with cardinality of the continuum by structures of Polish groups with two-sided (left or right) invariant Haar measures. By using this approach we answer positively Maleki’s certain question (2012) what are the real k-dimensional manifolds with at least two different Lie group structures that have the same Haar measure. It is demonstrated that for each diffused Borel probability measure defined in a Polish space (G;ρ ;B ρ (G)) without isolated points there exist a metric ρ 1 and a group operation ⊙ in G such that B ρ (G) = B ρ1 (G) and (G;ρ 1 ;B ρ1 (G);⊙) stands a compact Polish group with a two-sided (left or right) invariant Haar measure μ , where B ρ (G) and B ρ1 (G) denote Borel σ-algebras of subsets of G generated by metrics ρ and ρ 1 , respectively. Similar approach is used for a construction of locally compact non-compact or non-locally compact Polish groups equipped with two-sided (left or right) invariant quasi-finite Borel measures." @default.
- W2463762018 created "2016-07-22" @default.
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- W2463762018 date "2016-06-01" @default.
- W2463762018 modified "2023-09-25" @default.
- W2463762018 title "Equipment of Sets with Cardinality of the Continuum by Structures of Polish Groups with Haar Measures" @default.
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- W2463762018 doi "https://doi.org/10.18052/www.scipress.com/ijarm.5.8" @default.
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