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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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/