The McShane and the Pettis integral of Banach space-valued functions defined on ${\Bbb R}\sp m$
Ye, Guoju ; Schwabik, Štefan
Illinois J. Math., Tome 46 (2002) no. 3, p. 1125-1144 / Harvested from Project Euclid
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In this paper, we define and study the McShane integral of functions mapping a compact interval $I_0$ in $R^m$ into a Banach space $X$. We compare this integral with the Pettis integral and prove, in particular, that the two integrals are equivalent if $X$ is reflexive and the unit ball of the dual $X^*$ satisfies an additional condition (P). This gives additional information on an implicitly stated open problem of R.A. Gordon and on the work of D.H. Fremlin and J. Mendoza.
Publié le : 2002-10-15
Classification:  28B05,  26A39,  46G10 
@article{1258138470,
     author = {Ye, Guoju and Schwabik, \v Stefan},
     title = {The McShane and the Pettis integral of Banach space-valued functions defined on ${\Bbb R}\sp m$},
     journal = {Illinois J. Math.},
     volume = {46},
     number = {3},
     year = {2002},
     pages = { 1125-1144},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1258138470}
}

Ye, Guoju; Schwabik, Štefan. The McShane and the Pettis integral of Banach space-valued functions defined on ${\Bbb R}\sp m$. Illinois J. Math., Tome 46 (2002) no. 3, pp.  1125-1144. http://gdmltest.u-ga.fr/item/1258138470/