# 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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