Please use this identifier to cite or link to this item: http://hdl.handle.net/10525/408

 Title: On Averaging Null Sequences of Real-Valued Functions Authors: Kiriakouli, P. Ch. Keywords: Partition TheoremsUniform ConvergenceRepeated Averages of Real-Valued FunctionsConvergence IndexOscillation Index Issue Date: 2000 Publisher: Institute of Mathematics and Informatics Citation: Serdica Mathematical Journal, Vol. 26, No 2, (2000), 79p-104p Abstract: If ξ is a countable ordinal and (fk) a sequence of real-valued functions we define the repeated averages of order ξ of (fk). By using a partition theorem of Nash-Williams for families of finite subsets of positive integers it is proved that if ξ is a countable ordinal then every sequence (fk) of real-valued functions has a subsequence (f'k) such that either every sequence of repeated averages of order ξ of (f'k) converges uniformly to zero or no sequence of repeated averages of order ξ of (f'k) converges uniformly to zero. By the aid of this result we obtain some results stronger than Mazur’s theorem. URI: http://hdl.handle.net/10525/408 ISSN: 1310-6600 Appears in Collections: Volume 26 Number 2

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