Remote Access Bulletin of the American Mathematical Society

Bulletin of the American Mathematical Society

ISSN 1088-9485(online) ISSN 0273-0979(print)

 

 

A cantor function constructed by continued fractions


Authors: F. Herzog and B. H. Bissinger
Journal: Bull. Amer. Math. Soc. 53 (1947), 104-115
DOI: https://doi.org/10.1090/S0002-9904-1947-08749-8
MathSciNet review: 0019695
Full-text PDF Free Access

References | Additional Information

References [Enhancements On Off] (What's this?)

  • 1. F. Bernstein, Über eine Anwendung der Mengenlehre auf ein aus der Theorie der säkularen Störungen herrührendes Problem, Math. Ann. vol. 71 (1912) pp. 417-439.
  • 2. C. Carathéodory, Vorlesungen über reelle Funktionen, Leipzig and Berlin, 1927.
  • 3. R. E. Gilman, A class of functions continuous but not absolutely continuous, Ann. of Math. (2) 33 (1932), no. 3, 433–442. MR 1503068, https://doi.org/10.2307/1968527
  • 4. F. Herzog and B. H. Bissinger, A generalization of Borel’s and F. Bernstein’s theorems on continued fractions, Duke Math. J. 12 (1945), 325–334. MR 0012346
  • 5. E. Hille and J. D. Tamarkin, Remarks on a Known Example of a Monotone Continuous Function, Amer. Math. Monthly 36 (1929), no. 5, 255–264. MR 1521732, https://doi.org/10.2307/2298506
  • 6. E. W. Hobson, The theory of functions of a real variable, vol. 1, Cambridge, 1927.
  • 7. G. Kowalewski, Grundzüge der Differential- und Integralrechnung, Leipzig and Berlin, 1928.
  • 8. O. Perron, Die Lehre von den Kettenbrüchen, Leipzig and Berlin, 1929.


Additional Information

DOI: https://doi.org/10.1090/S0002-9904-1947-08749-8