Abstract
It is proved that the setwise limit of a bounded sequence of signed topological measures is a signed topological measure; here the signed measures and proper signed topological measures which are the components of the decomposition of the members of the sequence setwise converge to the corresponding components of the decomposition of the limit signed topological measure. The results thus obtained give a negative answer to the question concerning the possibility to represent a regular Borel measure (nonzero) as a setwise limit of a sequence of proper topological measures.
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Svistula, M. On the setwise convergence of sequences of signed topological measures. Arch. Math. 100, 191–200 (2013). https://doi.org/10.1007/s00013-013-0485-4
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DOI: https://doi.org/10.1007/s00013-013-0485-4