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Some properties of functions connected with a Cantor like set. (English) Zbl 0839.26006

The author defines a Cantor like set \(C_k\), \(k\in \mathbb{N}\): starting from \([0, 1]\), at each step one divides each interval in \(2k+ 1\) equal parts and remove the open subintervals at even positions. (\(C_1\) is the standard Cantor set.) Then two functions \(f, \nu: [0, 1]\to C_k\) are introduced with some special properties: for example, \(f\) is midway convex for any two points belonging to \(C_k\).

MSC:

26A30 Singular functions, Cantor functions, functions with other special properties
28A05 Classes of sets (Borel fields, \(\sigma\)-rings, etc.), measurable sets, Suslin sets, analytic sets
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