منابع مشابه
Coding into Ramsey Sets
In [6] W. T. Gowers formulated and proved a Ramseytype result which lies at the heart of his famous dichotomy for Banach spaces. He defines the notion of weakly Ramsey set of block sequences of an infinite dimensional Banach space and shows that every analytic set of block sequences is weakly Ramsey. We show here that Gowers’ result follows quite directly from the fact that all Gδ sets are weak...
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We study the family of rational sets of words, called completely reducible and which are such that the syntactic representation of their characteristic series is completely reducible. This family contains, by a result of Reutenauer, the submonoids generated by bifix codes and, by a result of Berstel and Reutenauer, the cyclic sets. We study the closure properties of this family. We prove a resu...
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Let G be a compact abelian group and let T be the character group of G. Suppose £ is a subset of T. A trigonometric polynomial f on G is said to be an ^-polynomial if its Fourier transform / vanishes off E. The set E is said to be a Sidon set if there is a positive number B such that 2^xeb |/(X)| á-B||/||u for all E-polynomials /; here, ||/||„ = sup{ |/(x)| : xEG}. In this note we shall discuss...
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We prove that Julia sets are uniformly perfect in the sense of Pommerenke (Arch. Math. 32 (1979), 192-199). This implies that their linear density of loganthmic capacity is strictly positive, thus implying that Julia sets are regular in the sense of Dinchlet. Using this we obtain a formula for the entropy of invanant harmonic measures on Julia sets. As a corollary we give a very short proof of ...
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It is shown that Matet’s characterization ([9]) of the Ramsey property relative to a selective co-ideal H, in terms of games of Kastanas ([6]), still holds if we consider semiselectivity ([3]) instead of selectivity. Moreover, we prove that a co-ideal H is semiselective if and only if Matet’s game-theoretic characterization of the H-Ramsey property holds. This lifts Kastanas’s characterization ...
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ژورنال
عنوان ژورنال: Colloquium Mathematicum
سال: 1993
ISSN: 0010-1354,1730-6302
DOI: 10.4064/cm-64-2-163-171