Conditions for the absence of jumps of the solution to the adjoint system of the maximum principle for optimal control problems with state constraints

Properties of Lagrange multipliers from the Pontryagin maximum principle for problems with state constraints are investigated. Sufficient conditions for the continuity of the solution of the adjoint solution depending on how the extremal trajectory approaches the state constraint boundary are obtained. The proof uses the notion of closure by measure of a Lebesgue measurable function and the Caratheodory theorem.