Internal characterization of Brezis-Lieb spaces

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Emelyanov E. Y. , Marabeh M. A. A.

POSITIVITY, vol.24, no.3, pp.585-592, 2020 (Journal Indexed in SCI) identifier identifier

  • Publication Type: Article / Article
  • Volume: 24 Issue: 3
  • Publication Date: 2020
  • Doi Number: 10.1007/s11117-019-00695-z
  • Title of Journal : POSITIVITY
  • Page Numbers: pp.585-592


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).