منابع مشابه
Sweeping out on a Set of Integers
Let (X, ®, m) be a Lebesgue space, m(X) = 1, and let T be an invertible measurable nonsingular aperiodic transformation of X onto X. If S is a set of r integers, r > 2, then there exists a set A of measure less than /•"' S*_! k~l such that X = U,es T"A. Thus for every infinite set of integers W there exist sets A of arbitrarily small measure such that X = U nniv T"A.
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For r-~2 let p(n, r ) denote the maximum cardinality of a subset A of N = { 1 , 2 . . . . , n} such that there are no B c A and an integer y with S b = y ' . I t is shown that for any e >-0 and bEB n>-n(e), (l+o(l))2~/t'+l>n('-l>/t'+l)~_p(n, r)~_n~§ for all r_~5, and that for every fixed r~_6, p(n,r)=(l+o(1)).21/t'+~)n (~-1)/('§ as n ~ . Let f(n,m) denote t h e m a x i m u m c a r d i n a l i t...
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ژورنال
عنوان ژورنال: Proceedings of the American Mathematical Society
سال: 1978
ISSN: 0002-9939
DOI: 10.2307/2042461