Abstract
We study topological and categorical aspects of the extension of σ -additive measures from a field of sets to the generated σ -field within a category of Boolean algebras carrying initial sequential convergences with respect to 2 -valued homomorphisms. We describe the relationship between σ -additivity and sequential continuity of finitely additive measures. A key role is played by the epireflective subcategory of absolutely sequentially closed objects. In case of fields of sets such objects are exactly σ -fields. The results provide information about basic notions of probability theory: events, probability measures, and random functions.
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