On Functions of Finite Baire Index
Abstract
It is proved that every function of finite Baire index on a separable metric space $K$ is a $D$function, i.e., a difference of bounded semicontinuous functions on $K$. In fact it is a strong $D$function, meaning it can be approximated arbitrarily closely in $D$norm, by simple $D$functions. It is shown that if the $n^{th}$ derived set of $K$ is nonempty for all finite $n$, there exist $D$functions on $K$ which are not strong $D$functions. Further structural results for the classes of finite index functions and strong $D$functions are also given.
 Publication:

arXiv Mathematics eprints
 Pub Date:
 December 1993
 arXiv:
 arXiv:math/9312209
 Bibcode:
 1993math.....12209C
 Keywords:

 Mathematics  Functional Analysis;
 46B