On the Boolean algebra tensor product via Caratheodory spaces of place functions
Abstract
We show that the Carath\'eodory space of place functions on the free product of two Boolean algebras is Riesz isomorphic with Fremlin's Archimedean Riesz space tensor product of their respective Carath\'eodory spaces of place functions. We provide a solution to Fremlin's problem 315Y(f) in fremlinmeasure concerning completeness in the free product of Boolean algebras by applying our results on the Archimedean Riesz space tensor product to Carath\'eodory spaces of place functions.
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