Algebraic theory of measure algebras
A. Horn and A. Tarski initiated the abstract theory of measure algebras. Independently V. Sushchansky, B. Oliynyk and P. Cameron studied the direct limits of Hamming spaces. In the current paper, we introduce new examples of locally standard measure algebras and complete the classification of coun...
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| Datum: | 2023 |
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| Hauptverfasser: | , |
| Format: | Artikel |
| Sprache: | English |
| Veröffentlicht: |
Видавничий дім "Академперіодика" НАН України
2023
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| Schriftenreihe: | Доповіді НАН України |
| Schlagworte: | |
| Online Zugang: | http://dspace.nbuv.gov.ua/handle/123456789/192996 |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Zitieren: | Algebraic theory of measure algebras / O.O. Bezushchak, B.V. Oliynyk // Доповіді Національної академії наук України. — 2023. — № 2. — С. 3-9. — Бібліогр.: 13 назв. — англ. |
Institution
Digital Library of Periodicals of National Academy of Sciences of Ukraine| Zusammenfassung: | A. Horn and A. Tarski initiated the abstract theory of measure algebras. Independently V. Sushchansky, B. Oliynyk
and P. Cameron studied the direct limits of Hamming spaces. In the current paper, we introduce new examples of
locally standard measure algebras and complete the classification of countable locally standard measure algebras.
Countable unital locally standard measure algebras are in one-to-one correspondence with Steinitz numbers. Given
a Steinitz number s such measure algebra is isomorphic to the Boolean algebra of s-periodic sequences of 0 and 1.
Nonunital locally standard measure algebras are parametrized by pairs (s, r), where s is a Steinitz number and r
is a real number greater or equal to 1. We also show that an arbitrary (not necessarily locally standard) measure
algebra is embeddable in a metric ultraproduct of standard Hamming spaces. In other words, an arbitrary measure
algebra is sofic. |
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