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Title: On Averaging Null Sequences of Real-Valued Functions
Authors: Kiriakouli, P. Ch.
Keywords: Partition Theorems
Uniform Convergence
Repeated Averages of Real-Valued Functions
Convergence Index
Oscillation 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.
ISSN: 1310-6600
Appears in Collections:Volume 26 Number 2

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