Journal of the Chungcheong Mathematical Society (충청수학회지)

The Chungcheong Mathematical Society (충청수학회)
권호 표지
DOI QR코드

DOI QR Code

A GENERALIZED SINGULAR FUNCTION

  • Baek, In-Soo (Department of Mathematics Pusan University of Foreign Studies)
  • Received : 2010.05.31
  • Accepted : 2010.08.12
  • Published : 2010.12.30
Download PDF
⟨ Previous Next ⟩

Abstract

We study a singular function which we call a generalized cylinder convex(concave) function induced from different generalized dyadic expansion systems on the unit interval. We show that the generalized cylinder convex(concave)function is a singular function and the length of its graph is 2. Using a local dimension set in the unit interval, we give some characterization of the distribution set using its derivative, which leads to that this singular function is nowhere differentiable in the sense of topological magnitude.

Keywords

References

  1. I. S. Baek, Derivative of the Riesz-Nagy-Takacs function, Bull. Kor. Math. Soc., to appear.
  2. P. Billingsley, Probabilitity and Measure, John Wiley and Sons, 1995.
  3. L. Olsen, Extremely non-normal numbers, Math. Proc. Camb. Phil. Soc. 137 (2004), 43-53. https://doi.org/10.1017/S0305004104007601
  4. J.Paradis, P. Viader and L. Bilibiloni, Riez-Nagy singular functions revisited, J. Math. Anal. Appl. 329 (2007), 592-602. https://doi.org/10.1016/j.jmaa.2006.06.082
  5. H. L. Royden, Real Analysis, Macmillan Publishing Company, 1988.