On the approximately continuous Denjoy integral
نویسندگان
چکیده
منابع مشابه
The distributional Denjoy integral
Let f be a distribution (generalised function) on the real line. If there is a continuous function F with real limits at infinity such that F ′ = f (distributional derivative) then the distributional integral of f is defined as ∫ ∞ −∞ f = F (∞)−F (−∞). It is shown that this simple definition gives an integral that includes the Lebesgue and Henstock–Kurzweil integrals. The Alexiewicz norm leads ...
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As is well-known, there exist various definitions of the double Denjoy integral (see [1,2,5]). Conditions for passage of limits through these integrals have not yet been studied. The object of this paper is to investigate the conditions for passage of the limit through the double Denjoy integral defined by V.G. Chelidze (see [7]). Here we shall use the well-known terms (see, for example, [8]). ...
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ژورنال
عنوان ژورنال: Tohoku Mathematical Journal
سال: 1963
ISSN: 0040-8735
DOI: 10.2748/tmj/1178243808