# On Averaging Null Sequences of Real-Valued Functions

Serdica Mathematical Journal (2000)

- Volume: 26, Issue: 2, page 79-104
- ISSN: 1310-6600

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topKiriakouli, 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 -

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