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Some propositions on diophantine approximation. (English) Zbl 0756.11019

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 \(x\).

MSC:

11J70 Continued fractions and generalizations
11J04 Homogeneous approximation to one number
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