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On the Dimension of the Space of Weakly Additive Functionals

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Abstract

Important demanded properties of weakly additive order-preserving normalized functionals are established. Various interpretations of a weakly additive order-preserving normalized functional are given. The continuity of such a functional as a function depending on a set in a given compact space is proved. Based on these results, an example is constructed showing that the space \(O(X)\) of weakly additive order-preserving normalized functionals is not embedded in any space of finite (or even countable) algebraic dimension, provided that the compact space \(X\) contains more than one point.

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  1. Nukus State Pedagogical Institute, Nukus, 230100, Uzbekistan

    R. E. Jiemuratov

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  1. R. E. Jiemuratov
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Correspondence to R. E. Jiemuratov.

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Translated from Matematicheskie Zametki, 2023, Vol. 113, pp. 347–359 https://doi.org/10.4213/mzm13540.

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Jiemuratov, R.E. On the Dimension of the Space of Weakly Additive Functionals. Math Notes 113, 345–355 (2023). https://doi.org/10.1134/S0001434623030045

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