On Averaging Null Sequences of Real-Valued Functions

Kiriakouli, P. Ch.. "On Averaging Null Sequences of Real-Valued Functions." Serdica Mathematical Journal 26.2 (2000): 79-104. <http://eudml.org/doc/11481>.

@article{Kiriakouli2000,
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.},
author = {Kiriakouli, P. Ch.},
journal = {Serdica Mathematical Journal},
keywords = {Partition Theorems; Uniform Convergence; Repeated Averages of Real-Valued Functions; Convergence Index; Oscillation Index; partition theorems; uniform convergence; repeated averages of real-valued functions; convergence index; oscillation index},
language = {eng},
number = {2},
pages = {79-104},
publisher = {Institute of Mathematics and Informatics},
title = {On Averaging Null Sequences of Real-Valued Functions},
url = {http://eudml.org/doc/11481},
volume = {26},
year = {2000},
}

TY - JOUR
AU - Kiriakouli, P. Ch.
TI - On Averaging Null Sequences of Real-Valued Functions
JO - Serdica Mathematical Journal
PY - 2000
PB - Institute of Mathematics and Informatics
VL - 26
IS - 2
SP - 79
EP - 104
AB - 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.
LA - eng
KW - Partition Theorems; Uniform Convergence; Repeated Averages of Real-Valued Functions; Convergence Index; Oscillation Index; partition theorems; uniform convergence; repeated averages of real-valued functions; convergence index; oscillation index
UR - http://eudml.org/doc/11481
ER -