Continuity of Symmetrically Continuous functions
by
Marcin Szyszkowski
West Virginia University

 begindocument A function f:A --> R where A subset R is symmetrically continuous at a point x if for every \epsilon > 0 there is \delta > 0 such that if 0 < h < \delta and x +/- h in A then |f(x+h)-f(x-h)| < \epsilon. We show that if f is symmetrically continuous on a measurable or Baire measurable set then f is continuous almost everywhere on that set. We also discuss some extension properties of symmetrically continuous and continuous functions.

Date received: February 9, 1998