For a multidimensional control problem (P)K involving controls u ∈ L∞, we construct a dual problem (D)K in which the variables ν to be paired with u are taken from the measure space rca (Ω, B) instead of (L∞)∗. For this purpose, we add to (P)K a Baire class restriction for the representatives of the controls u. As main results, we prove a strong duality theorem and saddle-point conditions.