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Vladikavkaz. Mat. Zh., 2016, Volume 18, Number 1, Pages 21–25 (Mi vmj568)  

This article is cited in 6 scientific papers (total in 6 papers)

Two measure-free versions of the Brezis–Lieb lemma

E. Yu. Emelyanovab, M. A. A. Marabehb

a Sobolev Institute of Mathematics, Laboratory of Functional Analysis, 4 Koptyug Avenue, Novosibirsk, 630090, Russia
b Middle East Technical University, Department of Mathematics, Turkey, 06800, Ankara, Dumlupinar Bulvari, 1

Abstract: We present two measure-free versions of the Brezis–Lieb lemma for $uo$-convergence in Riesz spaces.

Key words: Brezis–Lieb lemma, uniformly integrable sequence, Riesz space, $uo$-convergence, almost order bounded set, $\sigma uo$-continuous mapping.

Funding Agency Grant Number
Middle East Technical University BAP-01-01-2016-001
This research was funded by Middle East Technical University BAP, research project № BAP-01-01-2016-001.


Full text: PDF file (182 kB)
References: PDF file   HTML file
UDC: 517.98
MSC: 28A20, 46E30, 46B42
Received: 11.01.2016
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Citation: E. Yu. Emelyanov, M. A. A. Marabeh, “Two measure-free versions of the Brezis–Lieb lemma”, Vladikavkaz. Mat. Zh., 18:1 (2016), 21–25

Citation in format AMSBIB
\Bibitem{EmeMar16}
\by E.~Yu.~Emelyanov, M.~A.~A.~Marabeh
\paper Two measure-free versions of the Brezis--Lieb lemma
\jour Vladikavkaz. Mat. Zh.
\yr 2016
\vol 18
\issue 1
\pages 21--25
\mathnet{http://mi.mathnet.ru/vmj568}


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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. M. Kandic, M. A. A. Marabeh, V. G. Troitsky, “Unbounded norm topology in Banach lattices”, J. Math. Anal. Appl., 451:1 (2017), 259–279  crossref  mathscinet  zmath  isi  scopus
    2. È. Yu. Emel'yanov, Y. Dabboorasad, “Unbounded convergence in the convergence vector lattices: a survey”, Vladikavk. matem. zhurn., 20:2 (2018), 49–56  mathnet  crossref
    3. Y. A. Dabboorasad, E. Y. Emelyanov, M. A. A. Marabeh, “$u\tau$-convergence in locally solid vector lattices”, Positivity, 22:4 (2018), 1065–1080  crossref  mathscinet  zmath  isi  scopus
    4. Y. A. Dabboorasad, E. Y. Emelyanov, M. A. A. Marabeh, “Um-topology in multi-normed vector lattices”, Positivity, 22:2 (2018), 653–667  crossref  mathscinet  zmath  isi  scopus
    5. M. Marabeh, “The Brezis-Lieb lemma in convergence vector lattices”, Turk. J. Math., 42:3 (2018), 1436–1441  crossref  mathscinet  zmath  isi  scopus
    6. A. Aydin, S. Gorokhova, H. Gul, “Nonstandard hulls of lattice-normed ordered vector spaces”, Turk. J. Math., 42:1 (2018), 155–163  crossref  mathscinet  zmath  isi  scopus
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