Geodesic
Convergence theorems for the Birkhoff integral
Czechoslovak Mathematical Journal, Tome 58 (2008) no. 4, pp. 1207-1219

Voir la notice de l'article provenant de la source Czech Digital Mathematics Library

We give sufficient conditions for the interchange of the operations of limit and the Birkhoff integral for a sequence $(f_n)$ of functions from a measure space to a Banach space. In one result the equi-integrability of $f_n$'s is involved and we assume $f_n\to f$ almost everywhere. The other result resembles the Lebesgue dominated convergence theorem where the almost uniform convergence of $(f_n)$ to $f$ is assumed.
Classification : 28B05, 46G10
Keywords: Birkhoff integral; convergence theorems; vector valued functions 
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     author = {Balcerzak, Marek and Potyra{\l}a, Monika},
     title = {Convergence theorems for the {Birkhoff} integral},
     journal = {Czechoslovak Mathematical Journal},
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     zbl = {1174.28011},
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Balcerzak, Marek; Potyrała, Monika. Convergence theorems for the Birkhoff integral. Czechoslovak Mathematical Journal, Tome 58 (2008) no. 4, pp. 1207-1219. http://geodesic.mathdoc.fr/item/CMJ_2008__58_4_a24/