  We 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.
