On Averaging Null Sequences of Real-Valued Functions
Serdica Mathematical Journal, Tome 26 (2000) no. 2, pp. 79-104
Voir la notice de l'article provenant de la source Bulgarian Digital Mathematics Library
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.
Keywords:
Partition Theorems, Uniform Convergence, Repeated Averages of Real-Valued Functions, Convergence Index, Oscillation Index
@article{SMJ2_2000_26_2_a0,
author = {Kiriakouli, P. Ch.},
title = {On {Averaging} {Null} {Sequences} of {Real-Valued} {Functions}},
journal = {Serdica Mathematical Journal},
pages = {79--104},
publisher = {mathdoc},
volume = {26},
number = {2},
year = {2000},
language = {en},
url = {http://geodesic.mathdoc.fr/item/SMJ2_2000_26_2_a0/}
}
Kiriakouli, P. Ch. On Averaging Null Sequences of Real-Valued Functions. Serdica Mathematical Journal, Tome 26 (2000) no. 2, pp. 79-104. http://geodesic.mathdoc.fr/item/SMJ2_2000_26_2_a0/