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The Cantor function. (English) Zbl 1098.26006
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.

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