Factorization of the Baire equivalence through Baire envelopes

Determine whether the contravariant equivalence between Baire measurable spaces and commutative Pedersen–Baire envelopes (BaireMeas ≅ cPedBaireC) factors through the Baire envelope construction on Boolean algebras.

Background

The paper establishes a duality between Baire measurable spaces and commutative Pedersen–Baire envelope C*-algebras. Baire envelopes of Boolean algebras, however, correspond only to those Baire spaces arising from Stone spaces, so it is nontrivial whether the full equivalence passes through this intermediate construction.