The Henstock and McShane integrals of vector-valued functions
نویسندگان
چکیده
منابع مشابه
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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Results on integration by parts and integration by substitution for the variational integral of Henstock are well-known. When real-valued functions are considered, such results also hold for the Generalized Riemann Integral defined by Kurzweil since, in this case, the integrals of Kurzweil and Henstock coincide. However, in a Banach-space valued context, the Kurzweil integral properly contains ...
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ژورنال
عنوان ژورنال: Illinois Journal of Mathematics
سال: 1994
ISSN: 0019-2082
DOI: 10.1215/ijm/1255986726