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Prokhorov-like conditions for weak compactness of sets of bounded Radon measures on different topological spacesстатья Электронная публикация
- Авторы: Zakharov Valeriy K., Rodionov Timofey V.
- Сборник: ArXiv:math.FA
- Серия: Series arxive "math"
- Том: 1906
- Год издания: 2019
- Место издания: Cornell University Library Cornell University
- Первая страница: 1
- Последняя страница: 21
- DOI: 10.48550/arXiv.1906.03658
- Аннотация: The paper presents some weak compactness criterion for a subset~$M$ of the set $\RM_b(T,\cG)$ 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 $C_b(T,\cG)$ of all bounded continuous functions on~$T$ can be trivial and so does not separate points and closed sets, instead of $C_b(T,\cG)$-weak compactness we consider $S(T,\cG)$-weak compactness with respect to the new uniformly closed linear space $S(T,\mathcal{G})$ of all (symmetrizable) metasemicontinuous functions.The $S(T,\cG)$-weak topology on $\RM_b(T,\cG)$ is much weaker than the known topology~$\mathcal{T}_s$ of setwise convergence with respect to the $\si$-algebra~$\cB$ of all Borel subset of~$T$.
- Добавил в систему: Родионов Тимофей Викторович