A New Characterization of Baire Class 1 Functions

Abstract

We give a new characterization of the Baire class $1$ functions (defined on an ultrametric space) by proving that they are exactly the pointwise limits of sequences of full functions, which are particularly simple Lipschitz functions. Moreover we highlight the link between the two classical stratifications of the Borel functions by showing that the Baire class functions of some level are exactly those obtained as uniform limits of sequences of Delta functions of a corresponding level.