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On Some Properties of Infinite Iterations of the Functor of Idempotent Probability Measures

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Abstract

In this article, we consider the sets \(I(X),P(X)\in\mathbb{R}^{C(X)}\), where \(I(X)\) is the set of all idempotent probability measures on a compact Hausdorff space \(X\) and \(P(X)\) is the set of all probability measures equipped with the point-wise convergence topology. The uniform metrizability of the functor \(\mathcal{F}\) of idempotent probability measures \(I\) amd \(P\) is studied. It is proved that the functor of idempotent probability measures, acting in the category of compact Hausdorff spaces and in their continuous mappings, is perfect metrizable.

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Authors and Affiliations

  1. Tashkent institute of architecture and civil engineering, 100011, Tashkent, Uzbekistan

    A. A. Zaitov

  2. Chirchik state pedagogical institute, 111700, Chirchik town, Uzbekistan

    A. A. Zaitov

  3. National Research University Tashkent Institute of Irrigation and Agricultural Mechanization Engineers, 100000, Tashkent, Uzbekistan

    Kh. F. Kholturayev

Authors
  1. A. A. Zaitov
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  2. Kh. F. Kholturayev
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Corresponding authors

Correspondence to A. A. Zaitov or Kh. F. Kholturayev.

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(Submitted by T. K. Yuldashev)

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Zaitov, A.A., Kholturayev, K.F. On Some Properties of Infinite Iterations of the Functor of Idempotent Probability Measures. Lobachevskii J Math 43, 2341–2348 (2022). https://doi.org/10.1134/S1995080222110324

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  • DOI: https://doi.org/10.1134/S1995080222110324

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