Geodesic
A Pointwise Selection Principle for Functions of a~Single Variable with Values in a~Uniform Space
Matematičeskie trudy, Tome 9 (2006) no. 1, pp. 176-204

Voir la notice de l'article provenant de la source Math-Net.Ru

Given a sequence of functions, from a subset of the real line into a Hausdorff uniform space, we present a new sufficient condition for the sequence to contain a pointwise convergent subsequence. This new condition is much more weaker than the available conditions on the boundedness of generalized variations of functions, and reads in terms of some growth of moduli of variation of the functions of the sequence. Moreover, using the notion of the moduli of variation we study proper functions (i. e. those having one-sided left and right limits at each point) with respect to a dense subset and show that the Helly type selection principles involving the boundedness of generalized variations of the functions of the sequence, which are new in the context of functions with values in a uniform space, are consequences of our main result on the existence of a pointwise convergent subsequence. 
@article{MT_2006_9_1_a8,
     author = {V. V. Chistyakov},
     title = {A {Pointwise} {Selection} {Principle} for {Functions} of {a~Single} {Variable} with {Values} in {a~Uniform} {Space}},
     journal = {Matemati\v{c}eskie trudy},
     pages = {176--204},
     publisher = {mathdoc},
     volume = {9},
     number = {1},
     year = {2006},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MT_2006_9_1_a8/}
}
TY  - JOUR
AU  - V. V. Chistyakov
TI  - A Pointwise Selection Principle for Functions of a~Single Variable with Values in a~Uniform Space
JO  - Matematičeskie trudy
PY  - 2006
SP  - 176
EP  - 204
VL  - 9
IS  - 1
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/MT_2006_9_1_a8/
LA  - ru
ID  - MT_2006_9_1_a8
ER  - 
%0 Journal Article
%A V. V. Chistyakov
%T A Pointwise Selection Principle for Functions of a~Single Variable with Values in a~Uniform Space
%J Matematičeskie trudy
%D 2006
%P 176-204
%V 9
%N 1
%I mathdoc
%U http://geodesic.mathdoc.fr/item/MT_2006_9_1_a8/
%G ru
%F MT_2006_9_1_a8
V. V. Chistyakov. A Pointwise Selection Principle for Functions of a~Single Variable with Values in a~Uniform Space. Matematičeskie trudy, Tome 9 (2006) no. 1, pp. 176-204. http://geodesic.mathdoc.fr/item/MT_2006_9_1_a8/