Let N be the set of all natural numbers, $2^N$ the set of all subsets of N with product topology and $\mu:2^N \rightarrow G$ an additive set function. Prove that $\mu$ is countably additive iff it is continuous where $G$ denotes a commutative Hausdorff complete topological group.
2026-03-28 14:55:27.1774709727
Countable additivity and continuity of measures
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