Guoju Ye (2006)
Mathematica Bohemica
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In this paper we give some complete characterizations of the primitive of strongly Henstock-Kurzweil integrable functions which are defined on with values in a Banach space.
Márcia Federson (2002)
Czechoslovak Mathematical Journal
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We slightly modify the definition of the Kurzweil integral and prove that it still gives the same integral.
Štefan Schwabik, Ye Guoju (2001)
Czechoslovak Mathematical Journal
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The classical Bochner integral is compared with the McShane concept of integration based on Riemann type integral sums. It turns out that the Bochner integrable functions form a proper subclass of the set of functions which are McShane integrable provided the Banach space to which the values of functions belong is infinite-dimensional. The Bochner integrable functions are characterized by using gauge techniques. The situation is different in the case of finite-dimensional valued vector...
Tuo-Yeong Lee (2005)
Mathematica Bohemica
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It is shown that a Banach-valued Henstock-Kurzweil integrable function on an -dimensional compact interval is McShane integrable on a portion of the interval. As a consequence, there exist a non-Perron integrable function and a continuous function such that for all .