When do McShane and Pettis integrals coincide?
Di Piazza, L. ; Preiss, D.
Illinois J. Math., Tome 47 (2003) no. 4, p. 1177-1187 / Harvested from Project Euclid
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We give a partial answer to the question in the title by showing that the McShane and Pettis integrals coincide for functions with values in super-reflexive spaces as well as for functions with values in $c_0(\Gamma)$. We also improve an example of Fremlin and Mendoza, according to which these integrals do not coincide in general, by showing that, at least under the Continuum Hypothesis, there is a scalarly negligible function which is not McShane integrable.
Publié le : 2003-10-15
Classification:  28B05,  26A39,  26E25,  46G10 
@article{1258138098,
     author = {Di Piazza, L. and Preiss, D.},
     title = {When do McShane and Pettis integrals coincide?},
     journal = {Illinois J. Math.},
     volume = {47},
     number = {4},
     year = {2003},
     pages = { 1177-1187},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1258138098}
}

Di Piazza, L.; Preiss, D. When do McShane and Pettis integrals coincide?. Illinois J. Math., Tome 47 (2003) no. 4, pp.  1177-1187. http://gdmltest.u-ga.fr/item/1258138098/