Oren, Ishai Admissible functions with multiple discontinuities. (English) Zbl 0533.28009 Isr. J. Math. 42, 353-360 (1982). Author’s abstract: Let \(T\) be the unit circle, \(\alpha\) irrational and \(F: T\to \mathbb R\) a step function. A necessary and sufficient condition for the skew of the \(\alpha\)-rotation by \(f\) (considered as taking values mod 1) to be minimal is given. Also, the boundedness of \(\sum^n_{i=1}f(x+i\alpha)-n\int_{\pi} f(z)\,dz\) as \(n\to \infty\) is resolved. Reviewer: A. Grincevičius (Vilnius) Cited in 3 ReviewsCited in 17 Documents MSC: 28C10 Set functions and measures on topological groups or semigroups, Haar measures, invariant measures Keywords:multiple discontinuities × Cite Format Result Cite Review PDF Full Text: DOI References: [1] Furstenberg, H.; Keynes, H.; Shapiro, L., Prime flows in topological dynamics, Isr. J. Math., 14, 26-38 (1973) · Zbl 0264.54030 · doi:10.1007/BF02761532 [2] W. H. Gottschalk and G. A. Hedlund,Topological dynamics, Am. Math. Soc. Colloq, Vol. 36, Providence, RI, 1955. · Zbl 0067.15204 [3] Peterson, K.; Shapiro, L., Induced flows, Trans. Am. Math. Soc., 177, 375-390 (1973) · Zbl 0229.54036 · doi:10.2307/1996604 [4] Veech, W. A., Topological dynamics, Bull. Am. Math. Soc., 83, 775-830 (1977) · Zbl 0384.28018 · doi:10.1090/S0002-9904-1977-14319-X 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.