On Functions of Finite Baire Index

It is proved that every function of finite Baire index on a separable metric spaceKis aD-function, i.e., a difference of bounded semi-continuous functions onK. In fact it is a strongD-function, meaning it can be approximated arbitrarily closely inD-norm, by simpleD-functions. It is shown that if thenth derived set ofKis non-empty for all finiten, there existD-functions onKwhich are not strongD-functions. Further structural results for the classes of finite index functions and strongD-functions are also given.