An involution of reals, discontinuous on rationals, and whose derivative vanishes a.e.

ULUDAĞ A. M. , Ayral H.

TURKISH JOURNAL OF MATHEMATICS, vol.43, no.3, pp.1770-1775, 2019 (Journal Indexed in SCI) identifier identifier

  • Publication Type: Article / Article
  • Volume: 43 Issue: 3
  • Publication Date: 2019
  • Doi Number: 10.3906/mat-1903-34
  • Title of Journal : TURKISH JOURNAL OF MATHEMATICS
  • Page Numbers: pp.1770-1775

Abstract

We study the involution of the real line, induced by Dyer's outer automorphism of PGL(2,Z). It is continuous at irrationals with jump discontinuities at rationals. We prove that its derivative exists almost everywhere and vanishes almost everywhere.