The automorphism group of the Lebesgue measure has no non-trivial subgroups of index \(<2^{\omega} \) (Q2868714)
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scientific article; zbMATH DE number 6239336
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | The automorphism group of the Lebesgue measure has no non-trivial subgroups of index \(<2^{\omega} \) |
scientific article; zbMATH DE number 6239336 |
Statements
18 December 2013
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Lebesgue measure
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automorphism group
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small index property
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Polish groups
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automatic continuity
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0.8780985
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0.8514228
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0.85043824
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0.8497324
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0.8471045
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0.84390014
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0.84246814
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The automorphism group of the Lebesgue measure has no non-trivial subgroups of index \(<2^{\omega} \) (English)
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The author shows that the automorphism group \(\mathrm{Aut}( [0, 1], \lambda )\) of the Lebesgue measure on the unit interval has no non-trivial subgroups of index less than \(2^\omega\). He also gives a proof of the result, proved in [\textit{I. Ben Yaacov} et al., Trans. Am. Math. Soc. 365, No. 7, 3877--3897 (2013; Zbl 1295.03026)] that every homomorphism of \(\mathrm{Aut}( [0, 1], \lambda )\) to any separable group is continuous.
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