2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/62149We study an optimal control problem in Bolza form and we consider the value function associated to this problem. We prove two verification theorems which ensure that, if a function $W$ satisfies some suitable weak continuity assumptions and a Hamilton-Jacobi-Bellman inequality outside a countably $\mathcal H^n$-rectifiable set, then it is lower or equal to the value function. These results can be used for optimal synthesis approach.29 pages, 3 figureOptimization and Control49K15;93C15;49L25text