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The convergence determining class of connected open sets in product spaces

Dieter Landers
1972 Proceedings of the American Mathematical Society  
It is proved in this paper that each sequence of measures with values in a topological group-defined on the Borel field of a finite or countable product of connected, locally connected, separable metric spaces-which is Cauchy convergent for all connected open sets is Cauchy convergent for all Borel sets, too.
doi:10.1090/s0002-9939-1972-0298718-x fatcat:xyskcaqd6za2fesuz7puyqqotq