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Isomorphic Classification of \(*\)-Algebras of Log-Integrable Measurable Functions

  • R. Z. Abdullaev
  • V. I. Chilin
Conference paper
Part of the Springer Proceedings in Mathematics & Statistics book series (PROMS, volume 264)

Abstract

Let \((\varOmega ,\mu )\) be a \(\sigma \)-finite measure space, and let \(L_0(\varOmega , \mu )\) be the \(*\)-algebra of all complex (real) valued measurable functions on \((\varOmega ,\mu )\). The \(*\)-subalgebra \(L_{\log }(\varOmega , \mu )=\{f \in L_0(\varOmega , \mu ): \int \limits _{\varOmega } \log (1+|f|)d\mu < + \infty \} \) of \(L_0(\varOmega , \mu )\) is called the algebra of log-integrable measurable functions on \((\varOmega ,\mu )\). Using the notion of passport of a normed Boolean algebra, we give the necessary and sufficient conditions for a \(*\)-isomorphism of two algebras of log-integrable measurable functions.

Keywords

Passport of Boolean algebra Isomorphism of Boolean algebras Equivalent measures Log-integrable functions 

References

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    Vladimirov, D.A.: Boolean Algebras. Nauka Publications, Moscow (1969). [in Russian]Google Scholar

Copyright information

© Springer Nature Switzerland AG 2018

Authors and Affiliations

  1. 1.Uzbek State University of World LanguagesTashkentUzbekistan
  2. 2.National University of UzbekistanTashkentUzbekistan

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