On the Strong McShane Integral of Functions with Values in a Banach Space |
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Authors: | Stefan Schwabik Ye Guoju |
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Institution: | (1) Matematicky ustav AV CR, Zitna 25, 115 67 Praha 1, Czech Republic;(2) Northwest Normal University, Lanzhou, People's Republic of China |
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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. |
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Keywords: | : Bochner integral strong McShane integral |
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