A local duality principle for the Baire classes of functions

A local dual of a Banach space X is a closed subspace of X^∗ that satisfies the properties that the principle of local reflexivity assigns to X as a subspace of X∗∗. We show that, for every ordinal 1?α?ω₁, the spaces Bα0,1] of bounded Baire functions of class α are local dual spaces of the space M0,1] of all Borel measures. As a consequence, we derive that each annihilator Bα^⊥0,1] is the kernel of a norm-one projection.