منابع مشابه
Ergodic Sets
Introduction. Ergodic sets were introduced by Kryloff and Bogoliouboff in 1937 in connection with their study of compact dynamical systems [16]. The purpose of this paper is to review some of the work that has since been done on the theory that centers around this notion, and to present a number of supplementary remarks, applications, and simplifications. For simplicity we shall confine attenti...
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We prove that a sumset of a TE subset of N (these sets can be viewed as “aperiodic” sets) with a set of positive upper density intersects any polynomial sequence. For WM sets (subclass of TE sets) we prove that the intersection has lower Banach density one. In addition we obtain a generalization of the latter result to the case of several polynomials.
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متن کاملPolynomial Largeness of Sumsets and Totally Ergodic Sets
We prove that a sumset of a TE subset of N (these sets can be viewed as “aperiodic” sets) with a set of positive upper density intersects any polynomial sequence. For WM sets (subclass of TE sets) we prove that the intersection has lower Banach density one. In addition we obtain a generalization of the latter result to the case of several polynomials.
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ژورنال
عنوان ژورنال: Bulletin of the American Mathematical Society
سال: 1952
ISSN: 0002-9904
DOI: 10.1090/s0002-9904-1952-09580-x