On the almost monotone convergence of sequences of continuous functions

• Autorzy: Zbigniew Grande
• Języki publikacji: EN

Abstrakty

EN

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.

Słowa kluczowe

EN

Almost monotone convergence; Continuity; Baire 1 class; Upper semicontinuity; Lower semicontinuity; Approximate continuity

Kategorie tematyczne

• 26A21: Classification of real functions; Baire classification of sets and functions
• 54C05: Continuous maps
• 26A15: Continuity and related questions (modulus of continuity, semicontinuity, discontinuities, etc.)

• Wydawca: De Gruyter Open
• Czasopismo: Open Mathematics
• Rocznik: 2011
• Tom: 9
• Numer: 4
• Strony: 772-777

Daty

wydano

2011-08-01

online

2011-05-26

Twórcy

autor

Zbigniew Grande

• Kazimierz Wielki University

Bibliografia

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• [7] Petruska G., Laczkovich M., A theorem on approximately continuous functions, Acta Math. Acad. Sci. Hungar., 1973, 24(3–4), 383–387 http://dx.doi.org/10.1007/BF01958051
• [8] Preiss D., Limits of approximately continuous functions, Czechoslovak Math. J., 1971, 21(96)(3), 371–372
• [9] Sikorski R., Real Functions I, Monografie Matematyczne, 35, PWN, Warszawa, 1958 (in Polish)
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Identyfikatory

DOI

10.2478/s11533-011-0030-2