| Autor: |
Gogi Pantsulaia |
| Rok vydání: |
2016 |
| Předmět: |
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| Zdroj: |
International Journal of Advanced Research in Mathematics. 5:8-22 |
| ISSN: |
2297-6213 |
| DOI: |
10.18052/www.scipress.com/ijarm.5.8 |
| Popis: |
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;Bρ(G)) without isolated points there exist a metric ρ1and a group operation ⊙ in G such that Bρ(G) = Bρ1(G) and (G;ρ1;Bρ1(G);⊙) stands a compact Polish group with a two-sided (left or right) invariant Haar measure μ , where Bρ(G) and Bρ1(G) denote Borel σ-algebras of subsets of G generated by metrics ρ and ρ1, 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. |
| Databáze: |
OpenAIRE |
| Externí odkaz: |
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