S. Schwabik, Matematicky ustav AV CR, Zitna 25, 115 67 Praha 1, Czech Republic, e-mail: schwabik@math.cas.cz; Ye Guoju, Northwest Normal University, Lanzhou, Peoples Republic of China, e-mail: yeguoju@math.cas.cz, yeguoju@21cn.com
Abstract: 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 functions.
Keywords: Bochner integral, strong McShane integral
Classification (MSC 2000): 28-02
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