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Internal characterization of Brezis-Lieb spaces

Emelyanov, E. Y.
Marabeh, M. A. A.
In order to find an extension of Brezis-Lieb's lemma to the case of nets, we replace the almost everywhere convergence by the unbounded order convergence and introduce the pre-Brezis-Lieb property in normed lattices. Then we identify a wide class of Banach lattices in which the Brezis-Lieb lemma holds true. Among other things, it gives an extension of the Brezis-Lieb lemma for nets in L-p for p is an element of[1,infinity).