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Dovgoshey, O.; Martio, O.; Ryazanov, V.; Vuorinen, M.

The Cantor function. (English) Zbl 1098.26006

Expo. Math. 24, No. 1, 1-37 (2006).
This is an excellent (survey) article focused on the Cantor ternary function. The authors summarize and discuss its various properties in the Chapters: 2. Singularity, measurability and representability by absolutely continuous function; 3. Subadditivity, the points of local convexity; 4. Characterizations by means of functional equations; 5. The Cantor function as a distribution function; 6. Calculations of moments and the length of the graph; 7. Some topological properties; 8. Dini’s derivatives; 9. Lebesgue’s derivatives; 10. Hölder continuity, distortion of Hausdorff dimension, \(s_c\)-densities.
Reviewer: Jozef Bobok (Praha)

Cited in 64 Documents

MSC:

26A30 Singular functions, Cantor functions, functions with other special properties
28A78 Hausdorff and packing measures
28A80 Fractals

Keywords:

singular functions; Cantor ternary function
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\textit{O. Dovgoshey} et al., Expo. Math. 24, No. 1, 1--37 (2006; Zbl 1098.26006)
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References:

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