English

On the Boolean algebra tensor product via Caratheodory spaces of place functions

Functional Analysis 2023-01-30 v1

Abstract

We show that the Carath\'{e}odory 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\'{e}odory spaces of place functions. We provide a solution to Fremlin's problem 315Y(f) in \cite{fremlin_measure} concerning completeness in the free product of Boolean algebras by applying our results on the Archimedean Riesz space tensor product to Carath\'{e}odory spaces of place functions.

Keywords

Cite

@article{arxiv.2301.11866,
  title  = {On the Boolean algebra tensor product via Caratheodory spaces of place functions},
  author = {Gerard Buskes and Page Thorn},
  journal= {arXiv preprint arXiv:2301.11866},
  year   = {2023}
}