Let f be a function defined on [0, 1] and taking values in a Banach space X. We show that the limit set IHK(f) of Henstock-Kurzweil integral sums is non-empty and convex when the function f has an integrable majorant and X is separable. In the same setting we give a complete description of the limit set.
Caponetti, D., Di Piazza, L., Kadets, V. (2014). Description of the limit set of Henstock-Kurzweil integral sums of vector-valued functions. JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 421(2), 1151-1162 [10.1016/j.jmaa.2014.07.050].
Description of the limit set of Henstock-Kurzweil integral sums of vector-valued functions
CAPONETTI, Diana;DI PIAZZA, Luisa;
2014-01-01
Abstract
Let f be a function defined on [0, 1] and taking values in a Banach space X. We show that the limit set IHK(f) of Henstock-Kurzweil integral sums is non-empty and convex when the function f has an integrable majorant and X is separable. In the same setting we give a complete description of the limit set.File in questo prodotto:
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