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Covering functions by countably many functions from some families

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dc.contributor.author Grande, Zbigniew
dc.date.accessioned 2014-03-10T11:04:39Z
dc.date.available 2014-03-10T11:04:39Z
dc.date.issued 2013-10
dc.identifier.citation Lithuanian Mathematical Journal en_US
dc.identifier.uri http://repozytorium.ukw.edu.pl/handle/item/423
dc.description.abstract Let A be a nonempty family of functions from R to R. A function f : R → R is said to be strongly countably A-function if there is a sequence (fn) of functions from A such that Gr(f) ⊂ n Gr(fn) (Gr(f) denotes the graph of f). If A is the family of all continuous functions, the strongly countable A-functions are called strongly countably continuous and were investigated in [Z. Grande and A. Fatz-Grupka, On countably continuous functions, Tatra Mt. Math. Publ., 28:57–63, 2004], [G. Horbaczewska, On strongly countably continuous functions, Tatra Mt. Math. Publ., 42:81– 86, 2009], and [T.A. Natkaniec, On additive countably continuous functions, Publ. Math., 79(1–2):1–6, 2011]. In this article, we prove that the families A(R) of all strongly countably A-functions are closed with respect to some operations in dependence of analogous properties of the families A, and, in particular, we show some properties of strongly countably differentiable functions, strongly countably approximately continuous functions, and strongly countably quasi-continuous functions. en_US
dc.language.iso en en_US
dc.publisher Springer Science + Business Media New York en_US
dc.relation.ispartofseries Vol. 53, No.4, 406 - 411;
dc.subject lebesgue measurability en_US
dc.subject Baire property en_US
dc.subject first Baire class en_US
dc.subject approximate continuity en_US
dc.subject differentiability en_US
dc.title Covering functions by countably many functions from some families en_US
dc.type Article en_US

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