On the almost monotone convergence of sequences of continuous functions
Open Mathematics (2011)
- Volume: 9, Issue: 4, page 772-777
- ISSN: 2391-5455
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topZbigniew Grande. "On the almost monotone convergence of sequences of continuous functions." Open Mathematics 9.4 (2011): 772-777. <http://eudml.org/doc/269235>.
@article{ZbigniewGrande2011,
abstract = {A sequence (f n)n of functions f n: X → ℝ almost decreases (increases) to a function f: X → ℝ if it pointwise converges to f and for each point x ∈ X there is a positive integer n(x) such that f n+1(x) ≤ f n (x) (f n+1(x) ≥ f n(x)) for n ≥ n(x). In this article I investigate this convergence in some families of continuous functions.},
author = {Zbigniew Grande},
journal = {Open Mathematics},
keywords = {Almost monotone convergence; Continuity; Baire 1 class; Upper semicontinuity; Lower semicontinuity; Approximate continuity; almost monotone convergence; continuity; upper semicontinuity; lower semicontinuity; approximate continuity},
language = {eng},
number = {4},
pages = {772-777},
title = {On the almost monotone convergence of sequences of continuous functions},
url = {http://eudml.org/doc/269235},
volume = {9},
year = {2011},
}
TY - JOUR
AU - Zbigniew Grande
TI - On the almost monotone convergence of sequences of continuous functions
JO - Open Mathematics
PY - 2011
VL - 9
IS - 4
SP - 772
EP - 777
AB - A sequence (f n)n of functions f n: X → ℝ almost decreases (increases) to a function f: X → ℝ if it pointwise converges to f and for each point x ∈ X there is a positive integer n(x) such that f n+1(x) ≤ f n (x) (f n+1(x) ≥ f n(x)) for n ≥ n(x). In this article I investigate this convergence in some families of continuous functions.
LA - eng
KW - Almost monotone convergence; Continuity; Baire 1 class; Upper semicontinuity; Lower semicontinuity; Approximate continuity; almost monotone convergence; continuity; upper semicontinuity; lower semicontinuity; approximate continuity
UR - http://eudml.org/doc/269235
ER -
References
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