Geodesic
On the strong McShane integral of functions with values in a Banach space
Czechoslovak Mathematical Journal, Tome 51 (2001) no. 4, pp. 819-828 Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

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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 functions.
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.
Classification : 26A39, 28-02, 28B05, 46G10
Keywords: Bochner integral; strong McShane integral 
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     title = {On the strong {McShane} integral of functions with values in a {Banach} space},
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Schwabik, Štefan; Guoju, Ye. On the strong McShane integral of functions with values in a Banach space. Czechoslovak Mathematical Journal, Tome 51 (2001) no. 4, pp. 819-828. http://geodesic.mathdoc.fr/item/CMJ_2001_51_4_a10/

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