A metric property of the Cantor expansions of real numbers and criteria for irrationality. (Eine metrische Eigenschaft der Cantorschen Entwicklungen der reellen Zahlen und Irrationalitätskriterien.) (German) Zbl 0139.27905


11K55 Metric theory of other algorithms and expansions; measure and Hausdorff dimension
11J72 Irrationality; linear independence over a field
Full Text: DOI EuDML Link


[1] I. Niven: Irrational numbers. Carus Monographs, 11, 1956. · Zbl 0070.27101
[2] A. Oppenheim: Criteria for irrationality of certain classes of numbers. Amer. Math. Monthly, 61 (1954), 235-241. · Zbl 0055.04503 · doi:10.2307/2306389
[3] P. H. Diananda A. Oppenheim: Criteria for irrationality of certain classes of numbers II. Amer. Math. Monthly, 62 (1955), 222-225. · Zbl 0064.28701 · doi:10.2307/2306689
[4] K. Knopp: Mengentheoretische Behandlung einiger Probleme der diophantischen Approximationen und der transfiniten Wahrscheinlichkeiten. Math. Ann. 95 (1926), 409 - 426. · doi:10.1007/BF01206618
[5] A. Rényi: A számjegyek eloszlása valós számok Cantor-féle elöállításaiban. Mat. lap., VII, 1-2 (1956), 77-100.
[6] P. Turán: ,,Faktoriálisos” számrendszerbeli,,számjegyek” eloszlásáról. Mat. lap., VII, 1 - 2 (1956), 71-76.
[7] G. Pólya G. Szegö: Aufgaben und Lehrsätze aus der Analysis I. (russische Übersetzung). Moskau, 1956. · Zbl 0060.12307
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.