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 ⩽ ω 1 , the spaces B α [ 0 , 1 ] of bounded Baire functions of class α are local dual spaces of the space M [ 0 , 1 ] of all Borel measures. As a consequence, we derive that each annihilator B α [ 0 , 1 ] ⊥ is the kernel of a norm-one projection.