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MR1107271 (92f:46045) 46E40 (46A08 46G10)
Drewnowski, Lech; Florencio, Miguel; Paúl, Pedro J. The space of Pettis integrable functions is barrelled. Proc. Amer. Math. Soc. 114 (1992), no. 3, 687--694.
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