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Article overview
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Prokhorov-like conditions for weak compactness of sets of bounded Radon measures on different topological spaces | Valeriy K. Zakharov
; Timofey V. Rodionov
; | Date: |
9 Jun 2019 | Abstract: | 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. The $S(T,mathcal{G})$-weak topology on
$mathfrak{RM}_b(T,mathcal{G})$ is much weaker than the known topology
$mathcal{T}_s$ of setwise convergence with respect to the $sigma$-algebra
$mathcal{B}$ of all Borel subset of $T$. | Source: | arXiv, 1906.3658 | Services: | Forum | Review | PDF | Favorites |
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