Semigroups of pathological sets (Q2288404)
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scientific article
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Semigroups of pathological sets |
scientific article |
Statements
Semigroups of pathological sets (English)
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17 January 2020
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The complements of the \(\sigma\)-algebras of Lebesgue-measurable sets and of sets with the Baire property on the real line do not form subrings or subalgebras of the power set of \(\mathbb{R}\). The author investigates whether these families contain substantial subsemigroups with respect to intersection and union. The principal results are that Vitali-type sets on the one hand and Bernstein sets on the other can indeed generate large semigroups.
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Baire property
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Lebesgue-measurable
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Vitali set
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Bernstein set
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semigroup of sets
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