Geodesic
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/}
}
TY  - JOUR
AU  - Kiriakouli, P. Ch.
TI  - On Averaging Null Sequences of Real-Valued Functions
JO  - Serdica Mathematical Journal
PY  - 2000
SP  - 79
EP  - 104
VL  - 26
IS  - 2
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/SMJ2_2000_26_2_a0/
LA  - en
ID  - SMJ2_2000_26_2_a0
ER  - 
%0 Journal Article
%A Kiriakouli, P. Ch.
%T On Averaging Null Sequences of Real-Valued Functions
%J Serdica Mathematical Journal
%D 2000
%P 79-104
%V 26
%N 2
%I mathdoc
%U http://geodesic.mathdoc.fr/item/SMJ2_2000_26_2_a0/
%G en
%F 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/