Some new types of filter limit theorems for topological group-valued measures (Q2510989)

In the first part of the paper the authors collect some known results for measures with values in a metrizable topological group. In the second part the authors present versions of the theorems of Schur, Vitali-Hahn-Saks, Nikodým, Brooks-Jewett and Dieudonné using the following concept of filter-convergence: Let \(\mathfrak{F}\) be a filter on \(\mathbb{N}\). Then \((x_n)_{n\in\mathbb{N}}\) \(\mathfrak{F}\)-converges to \(x_0\) if the set \(\{n\in\mathbb{N}: x_n\in U\}\) belongs to \(\mathfrak{F}\) for every neighbourhood \(U\) of \(x_0\). (Reviewer's remark: The authors informed the reviewer that they are preparing an ``Addendum'' containing some corrections.) (Editorial remark: For the addendum see [Zbl 1408.28005].)