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

ULUDAĞ A. M., Ayral H.

TURKISH JOURNAL OF MATHEMATICS, cilt.43, sa.3, ss.1770-1775, 2019 (SCI-Expanded) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 43 Sayı: 3
  • Basım Tarihi: 2019
  • Doi Numarası: 10.3906/mat-1903-34
  • Dergi Adı: TURKISH JOURNAL OF MATHEMATICS
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus, TR DİZİN (ULAKBİM)
  • Sayfa Sayıları: ss.1770-1775
  • Anahtar Kelimeler: Involution, PGL, projective general linear group, continued fraction, derivative, discontinuity
  • Galatasaray Üniversitesi Adresli: Evet

Özet

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.