Displaying similar documents to “On normal numbers mod 2 ”

BV coboundaries over irrational rotations

Dalibor Volný (1997)

Studia Mathematica

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For every irrational rotation we construct a coboundary which is continuous except at a single point where it has a jump, is nondecreasing, and has zero derivative almost everywhere.

Aspects of uniformity in recurrence

Vitaly Bergelson, Bernard Host, Randall McCutcheon, Franiçois Parreau (2000)

Colloquium Mathematicae

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We analyze and cite applications of various, loosely related notions of uniformity inherent to the phenomenon of (multiple) recurrence in ergodic theory. An assortment of results are obtained, among them sharpenings of two theorems due to Bourgain. The first of these, which in the original guarantees existence of sets x,x+h, x + h 2 in subsets E of positive measure in the unit interval, with lower bounds on h depending only on m(E), is expanded to the case of arbitrary finite polynomial configurations...