Prokhorov-like conditions for weak compactness of sets of bounded Radon measures on different topological spaces
| Autor: | Zakharov, Valeriy K., Rodionov, Timofey V. |
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| Rok vydání: | 2019 |
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| Druh dokumentu: | Working Paper |
| Popis: | The paper presents some weak compactness criterion for a subset $M$ of the set $\mathfrak{RM}_b(T,\mathcal{G})$ of all positive bounded Radon measures on a Hausdorff topological space $(T,\mathcal{G})$ similar to the Prokhorov criterion for a complete separable metric space. Since for a general topological space the classical space $C_b(T,\mathcal{G})$ of all bounded continuous functions on $T$ can be trivial and so does not separate points and closed sets, instead of $C_b(T,\mathcal{G})$-weak compactness we consider $S(T,\mathcal{G})$-weak compactness with respect to the new uniformly closed linear space $S(T,\mathcal{G})$ of all (symmetrizable) metasemicontinuous functions. Comment: 20 pages; some notations and proofs (Lemmas 1 and 2, Proposition 2, Theorem 5 etc.) are simplified, some references to the literature are clarified, some typos removed |
| Databáze: | arXiv |
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