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.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Bruckner A.M., Differentiation of Real Functions, Lecture Notes in Math., 659, Springer, Berlin, 1978
Császár Á., Extensions of discrete and equal Baire functions, Acta Math. Hungar., 1990, 56(1–2), 93–99
Császár Á., Laczkovich M., Discrete and equal convergence, Stud. Sci. Math. Hung., 1975, 10(3–4), 463–472
Császár Á., Laczkovich M., Some remarks on discrete Baire classes, Acta Math. Acad. Sci. Hung., 1979, 33(1–2), 51–70
Császár Á., Laczkovich M., Discrete and equal Baire classes, Acta Math. Hungar., 1990, 55(1–2), 165–178
Grande Z., On discrete limits of sequences of approximately continuous functions and T ae-continuous functions, Acta Math. Hungar., 2001, 92(1–2), 39–50
Petruska G., Laczkovich M., A theorem on approximately continuous functions, Acta Math. Acad. Sci. Hungar., 1973, 24(3–4), 383–387
Preiss D., Limits of approximately continuous functions, Czechoslovak Math. J., 1971, 21(96)(3), 371–372
Sikorski R., Real Functions I, Monografie Matematyczne, 35, PWN, Warszawa, 1958 (in Polish)
Tall F.D., The density topology, Pacific J. Math., 1976, 62(1), 275–284
Author information
Authors and Affiliations
Corresponding author
About this article
Cite this article
Grande, Z. On the almost monotone convergence of sequences of continuous functions. centr.eur.j.math. 9, 772–777 (2011). https://doi.org/10.2478/s11533-011-0030-2
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.2478/s11533-011-0030-2