Mathematics, Department of
Date of this Version
1918
Abstract
Recently G. C. Young and A. Denjoy have communicated theorems—those in Denjoy's memoir are of an especially comprehensive character—dealing, in particular, with point sets where the four derivatives of a given continuous function are identical. It is the purpose of this note to treat an analogous problem that arises when "derivative" is replaced by "saltus." However, instead of confining ourselves to "saltus," we prove a more general theorem that applies essentially to all semi-continuous functions. We preface the proof of this theorem with the following
Comments
Published in Bull. Amer. Math. Soc. 24 (1918) 381-383.