Tsuchikura, Tamotsu Some propositions on diophantine approximation. (English) Zbl 0756.11019 Math. J. Toyama Univ. 14, 163-166 (1991). The author gives an equivalent statement to the following conjecture of Steinhaus: If \(\{f_ n\}\) is a sequence of measurable functions of period 1 and uniformly bounded then \(\limsup_{n} f_ n(nx)=\) constant for almost all \(x\). Reviewer: G.Larcher (Salzburg) MSC: 11J70 Continued fractions and generalizations 11J04 Homogeneous approximation to one number Keywords:conjecture of Steinhaus; approximation of one real PDFBibTeX XMLCite \textit{T. Tsuchikura}, Math. J. Toyama Univ. 14, 163--166 (1991; Zbl 0756.11019)