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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


MSC:

11K55 Metric theory of other algorithms and expansions; measure and Hausdorff dimension
11J72 Irrationality; linear independence over a field
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References:

[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
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