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Quasi-Invariant and Invariant Functionals and Measures on Systems of Topological Loops and Quasigroups

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Abstract

Under study are the left-invariant, right-invariant, and quasi-invariant functionals and measures on topological loops and quasigroups. We also address the relations between topologies and measures on loops, the left-invariant, right-invariant, and quasi-invariant functionals and measures on locally connected as well as profinite loops and quasigroups. Moreover, we inspect how the quasi-invariant measures on topological spaces are related to the loop or quasigroup actions on them. Also, we consider the continuations of quasi-invariant functionals and measures on the extensions of topological spaces as well as measures and functionals on the inverse spectra of topological loops and quasigroups.

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Authors and Affiliations

  1. MIREA–Russian Technological University, Moscow, Russia

    S. V. Ludkovsky

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  1. S. V. Ludkovsky
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Correspondence to S. V. Ludkovsky.

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Translated from Sibirskii Matematicheskii Zhurnal, 2023, Vol. 64, No. 5, pp. 1032–1049. https://doi.org/10.33048/smzh.2023.64.511

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Ludkovsky, S.V. Quasi-Invariant and Invariant Functionals and Measures on Systems of Topological Loops and Quasigroups. Sib Math J 64, 1186–1199 (2023). https://doi.org/10.1134/S0037446623050117

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  • DOI: https://doi.org/10.1134/S0037446623050117

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