Abstract
We show that in an abelian topological group subseries convergence depends only on the Borel field generated by the topology. We also prove a result about measurability of a limit for a pointwise converging sequence of measurable mappings into an analytic topological space.
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References
Jens Peter Reus Christensen,On some properties of Effros Borel structure on spaces of closed subsets, Math. Anm.195 (1971), 17–23.
Jens Peter Reus Christensen,Borel structures and a topological zero-onz law. Math. Scand.29 (1971), 245–255.
Frolik,A metrizable map with analytic domain and metrizable range is quotient, Bull. Amer. Math. Soc.76, (1970), 1112–1117.
J. Hoffmann-Jorgensen,The theory of analytic spaces, Various publications series nr. 10, Institute of Mathematics, Århus University, Denmark, 1970.
N. J. Kalton,Subseries convergence in topological groups and vector spaces. Israel J. Math.10 (1971), 402–411.
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Morch Andersen, N.J., Reus Christensen, J.P. Some results on Borel structures with applications to subseries convergence in abelian topological groups. Israel J. Math. 15, 414–420 (1973). https://doi.org/10.1007/BF02757080
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DOI: https://doi.org/10.1007/BF02757080