Banach-valued Henstock-Kurzweil integrable functions are McShane integrable on a portion
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Banach-valued Henstock-kurzweil Integrable Functions Are Mcshane Integrable on a Portion
It is shown that a Banach-valued Henstock-Kurzweil integrable function on an m-dimensional compact interval is McShane integrable on a portion of the interval. As a consequence, there exist a non-Perron integrable function f : [0, 1] −→ and a continuous function F : [0, 1] −→ such that
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and Applied Analysis 3 Then, as L[a, b] ⊂ HK([a, b]) it holds that dim(L[a, b]) ≤ dim(HK([a, b])) ≤ card(HK([a, b])). Therefore, by Lemma 8, Corollary 7 and the known fact that c0 = c, we obtain the desired conclusion. Hereafter, the Alexiewicz topology and the topology induced by the norm of Proposition 9 will be denoted as τ A and τ ‖⋅‖ , respectively. Proposition 10. The topology τ ‖⋅‖ on HK...
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ژورنال
عنوان ژورنال: Mathematica Bohemica
سال: 2005
ISSN: 0862-7959,2464-7136
DOI: 10.21136/mb.2005.134207