Number theoretical weak Bernoulli transformations on the unit interval. (English) Zbl 0548.10033
Let T be a transformation of the unit interval onto itself. Let there be a finite partition \(\cup_{i\in J}\Delta (i)\) of this interval such that T is continuous and one-to-one on each \(\Delta\) (i). Under several conditions, for which we must refer to the paper, it is shown that T is weak Bernoulli. The result is illustrated by some examples.
Reviewer: H.Jager
MSC:
11K16 | Normal numbers, radix expansions, Pisot numbers, Salem numbers, good lattice points, etc. |
28D05 | Measure-preserving transformations |