×

Density points of the Cantor sets. (Points de densité d’ensembles de Cantor.) (French) Zbl 0837.28003

The author gives a combinatorial characterization of the set of density points for a class of triadic Cantor sets with positive measure. This fact permits, incidentally, a verification of the classical density theorem of Lebesgue in the case of these particular subsets of \(\mathbb{R}\).

MSC:

28A05 Classes of sets (Borel fields, \(\sigma\)-rings, etc.), measurable sets, Suslin sets, analytic sets
03E05 Other combinatorial set theory
PDFBibTeX XMLCite
Full Text: DOI

References:

[1] Dence, Th, Differentiable points of the generalized Cantor-function, Rocky Mountain J. Math., 9, 239-249 (1979) · Zbl 0427.26004
[2] Lebesgue, H., Leçons sur l’Intégration et la Recherche des Fonctions Primitives (1904), Gauthier-Villars: Gauthier-Villars Paris · JFM 35.0377.01
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.