Geodesic
Bartle--Dunford--Schwartz Integral versus Bochner, Pettis and Dunford Integrals
Journal of convex analysis, Tome 20 (2013) no. 2, pp. 339-353.

Voir la notice de l'article provenant de la source Heldermann Verlag

We study some relationships between the Bartle-Dunford-Schwartz integral of a scalar valued function f , with respect to a vector measure m , and the Dunford, Pettis or Bochner integrals of its (vector valued) distribution function mf . The Dunford (or Pettis) integrability of mf is strongly related to the weak integrability (or the integrability) of f in the sense of Bartle-Dunford-Schwartz. In the case of the Bochner integrability of mf , a new function space appears. It is defined through the Choquet integrability of f with respect to the semivariation ||m|| of the measure m . We also study this space and present its main properties.
Classification : 46G10, 28B05, 46E30, 28B15
Mots-clés : Bartle-Dunford-Schwartz integral, Dunford integral, Pettis integral, Bochner integral, Choquet integral, vector measures 
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     author = {A. Fern\'andez and F. Mayoral and F. Naranjo},
     title = {Bartle--Dunford--Schwartz {Integral} versus {Bochner,} {Pettis} and {Dunford} {Integrals}},
     journal = {Journal of convex analysis},
     pages = {339--353},
     publisher = {mathdoc},
     volume = {20},
     number = {2},
     year = {2013},
     url = {http://geodesic.mathdoc.fr/item/JCA_2013_20_2_JCA_2013_20_2_a2/}
}
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A. Fernández; F. Mayoral; F. Naranjo. Bartle--Dunford--Schwartz Integral versus Bochner, Pettis and Dunford Integrals. Journal of convex analysis, Tome 20 (2013) no. 2, pp. 339-353. http://geodesic.mathdoc.fr/item/JCA_2013_20_2_JCA_2013_20_2_a2/