Displaying similar documents to “Classifications and characterizations of Baire-1 functions”

Characterizations of spreading models of l 1

Persephone Kiriakouli (2000)

Commentationes Mathematicae Universitatis Carolinae

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Rosenthal in [11] proved that if ( f k ) is a uniformly bounded sequence of real-valued functions which has no pointwise converging subsequence then ( f k ) has a subsequence which is equivalent to the unit basis of l 1 in the supremum norm. Kechris and Louveau in [6] classified the pointwise convergent sequences of continuous real-valued functions, which are defined on a compact metric space, by the aid of a countable ordinal index “ γ ”. In this paper we prove some local analogues of the above Rosenthal...

On the almost monotone convergence of sequences of continuous functions

Zbigniew Grande (2011)

Open Mathematics

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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.