Preserving affine Baire classes by perfect affine maps

Abstract

Let φ: X → Y be an affine continuous surjection between compact convex sets. Suppose that the canonical copy of the space of real-valued affine continuous functions on Y in the space of real-valued affine continuous functions on X is complemented. We show that if F is a topological vector space, then f : Y  → F is of affine Baire class α whenever the composition f ○ φ is of affine Baire class α. This abstract result is applied to extend known results on affine Baire classes of strongly affine Baire mappings.

Keywords: Vector-valued Baire function, strongly affine function