SOME COMMENTS ON AN APPROXIMATELY CONTINUOUS KHINTCHINE INTEGRAL

Abstract

The Khintchine integral is not comparable to the approximately continuous Perron integral. That is, there are functions that are integrable in one sense but not the other. There have been several attempts to define an integration process that includes both of these integrals. This paper points out an error in one of these proofs and defines another integration process that includes both of the integrals mentioned above.