Two measure-free versions of the Brezis - Lieb lemma
Автор: Emelyanov Eduard Yu., Marabeh Mohammad A. A.
Журнал: Владикавказский математический журнал @vmj-ru
Статья в выпуске: 1 т.18, 2016 года.
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We present two measure-free versions of the Brezis-Lieb lemma for uo-convergence in Riesz spaces.
Brezis-lieb lemma, uniformly integrable sequence, riesz space, uo-convergence, almost order bounded set, σuo-continuous mapping
Короткий адрес: https://sciup.org/14318524
IDR: 14318524
Список литературы Two measure-free versions of the Brezis - Lieb lemma
- Aliprantis C. D., Burkinshaw O. Positive operators. Orlando, Florida: Acad. Press, Inc., 1985. xvi+367 p. (Pure and Appl. Math. Vol. 119).
- Brezis H., Lieb E. A relation between pointwise convergence of functions and convergence of functionals//Proc. Amer. Math. Soc. 1983. Vol. 88, № 3. P. 486-490.
- Brezis H., Nirenberg L. Positive solutions of nonlinear elliptic equations involving critical Sobolev exponents//Comm. Pure Appl. Math. 1983. Vol. 36, № 4. P. 437-477.
- Gao N., Troitsky V., Xanthos F. Uo-convergence and its applications to Cesaro means in Banach lattices. Preprint, arXiv:1509.07914.
- Gao N., Xanthos F. Unbounded order convergence and application to martingales without probability//J. Math. Anal. Appl. 2014. Vol. 415, № 2. P. 931-947.
- Lieb E. Sharp constants in the Hardy-Littlewood-Sobolev and related inequalities//Ann. of Math. 1983. Vol. 118, № 2. P. 349-374.
- Luxemburg W. A. J., Zaanen A. C. Riesz Spaces. Vol. I. Amsterdam: North-Holland Publ. Comp., 1971. viii+514 p.
- Zaanen A. C. Riesz Spaces II//North-Holland Mathematical Library. Amsterdam: North-Holland Publ. Comp., 1983. xi+720 p.
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