E. Yu. Emelyanov, M. A. A. Marabeh, “Two measure-free versions of the Brezis–Lieb lemma”, Vladikavkaz. Mat. Zh., 18:1 (2016), 21

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Vladikavkazskii Matematicheskii Zhurnal, 2016, Volume 18, Number 1, Pages 21–25 (Mi vmj568)

This article is cited in 9 scientific papers (total in 9 papers)

Two measure-free versions of the Brezis–Lieb lemma

E. Yu. Emelyanov^ab, M. A. A. Marabeh^b

^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

Full-text PDF (182 kB) Citations (9)

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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.

Received: 11.01.2016

Document Type: Article

UDC: 517.98

MSC: 28A20, 46E30, 46B42

Language: English

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}

Linking options:

https://www.mathnet.ru/eng/vmj568

https://www.mathnet.ru/eng/vmj/v18/i1/p21

This publication is cited in the following 9 articles:

E. Y. Emelyanov, M. A. A. Marabeh, “Internal characterization of Brezis-Lieb spaces”, Positivity, 24:3 (2020), 585–592
E. Y. Emelyanov, S. G. Gorokhova, S. S. Kutateladze, “Unbounded order convergence and the Gordon theorem”, Vladikavk. matem. zhurn., 21:4 (2019), 56–62
R. Hadiji, F. Vigneron, “Existence of solutions of a non-linear eigenvalue problem with a variable weight”, J. Differ. Equ., 266:2-3 (2019), 1488–1513
A. M. Dabboorasad, E. Yu. Emelyanov, “Unbounded convergence in the convergence vector lattices: a survey”, Vladikavk. matem. zhurn., 20:2 (2018), 49–56
Y. A. Dabboorasad, E. Y. Emelyanov, M. A. A. Marabeh, “$u\tau$-convergence in locally solid vector lattices”, Positivity, 22:4 (2018), 1065–1080
Y. A. Dabboorasad, E. Y. Emelyanov, M. A. A. Marabeh, “Um-topology in multi-normed vector lattices”, Positivity, 22:2 (2018), 653–667
M. Marabeh, “The Brezis-Lieb lemma in convergence vector lattices”, Turk. J. Math., 42:3 (2018), 1436–1441
A. Aydin, S. Gorokhova, H. Gul, “Nonstandard hulls of lattice-normed ordered vector spaces”, Turk. J. Math., 42:1 (2018), 155–163
M. Kandic, M. A. A. Marabeh, V. G. Troitsky, “Unbounded norm topology in Banach lattices”, J. Math. Anal. Appl., 451:1 (2017), 259–279

Citing articles in Google Scholar: Russian citations, English citations
Related articles in Google Scholar: Russian articles, English articles

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References:	76

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