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

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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.
Classification : 26A39, 28-02, 28B05, 46G10
Keywords: Bochner integral; strong McShane integral 
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     author = {Schwabik, \v{S}tefan and Guoju, Ye},
     title = {On the strong {McShane} integral of functions with values in a {Banach} space},
     journal = {Czechoslovak Mathematical Journal},
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     zbl = {1002.28013},
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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/