2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/103878We show that if a product system comes from a quantum Markov semigroup, then it carries a natural Borel structure with respect to which the semigroup may be realized in terms of a measurable representation. We show, too, that the dual product system of a Borel product system also carries a natural Borel structure. We apply our analysis to study the order interval consisting of all quantum Markov semigroups that are subordinate to a given one.Revised according to the referee's comments and suggestions; to appear in International Journal of MathematicsOperator Algebras46L55, 46L53, 46L57, 46L60, 81S25, 47L90text