Sets of points of non-differentiability of absolutely continuous functions and of divergence of Fejér sums
✍ Scribed by A. S. Besicovitch
- Publisher
- Springer
- Year
- 1935
- Tongue
- English
- Weight
- 195 KB
- Volume
- 110
- Category
- Article
- ISSN
- 0025-5831
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📜 SIMILAR VOLUMES
## Abstract Let the Cantor set __C__ in ℝ be defined by __C__ = ∪^__r__^ ~__j__ =0~ __h~j~__ (__C__) with a disjoint union, where the __h~j~__ 's are similitude mappings with ratios 0 < __a~j~__ < 1. Let __μ__ be the self‐similar Borel probability measure on __C__ corresponding to the probability v
Let C ޒ denote the set of all continuous functions f : ޒ ª ޒ with 0 Ž n . n compact support. For a function f g C ޒ and measurable set A ; ޒ 0 Ž . let f, A denote the oscillation of f on A. We denote the Lebesgue Ž . n measure of A by A . Let K ; ޒ be a fixed symmetric convex set of 0 no