2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/214667There is a mathematical error in the first version of this paper. A new corrected version will be posted when the error is fixed, possibly with a modified title.There is a mathematical error in the first version of this paper. A new corrected version will be posted when the error is fixed, possibly with a modified titleProbabilitySemigroup inequalities, stochastic domination, Hardy's inequality, and strong ergodicitytext