E. Yu. Emelyanov, M. A. A. Marabeh, “Two measure-free versions of the Brezis–Lieb lemma”, Vladikavkaz. Mat. Zh., 2016, Volume 18, Number 1,Pages <nobr>21

This article is cited 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

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.

UDC: 517.98

MSC: 28A20, 46E30, 46B42

Received: 11.01.2016

Language: English