In the mathematical field of analysis, the Brezis–Lieb lemma is a basic result in measure theory. It is named for Haïm Brézis and Elliott Lieb, who discovered it in 1983. The lemma can be viewed as an improvement, in certain settings, of Fatou's lemma to an equality. As such, it has been useful for the study of many variational problems.
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| - Brezis–Lieb lemma (en)
- Лема Брезіса–Лієба (uk)
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| - In the mathematical field of analysis, the Brezis–Lieb lemma is a basic result in measure theory. It is named for Haïm Brézis and Elliott Lieb, who discovered it in 1983. The lemma can be viewed as an improvement, in certain settings, of Fatou's lemma to an equality. As such, it has been useful for the study of many variational problems. (en)
- У математичному аналізі лема Брезіса–Лієба є основним результатом в теорії міри. Вона названа на честь та , які довели її в 1983 році. Лему можна розглядати за певних умов як покращення леми Фату до рівності. Вона була корисна при дослідженні багатьох варіаційних проблем. (uk)
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| - Elliott H. Lieb and Michael Loss. Analysis. Second edition. Graduate Studies in Mathematics, 14. American Mathematical Society, Providence, RI, 2001. xxii+346 pp. (en)
- Michel Willem. Minimax theorems. Progress in Nonlinear Differential Equations and their Applications, 24. Birkhäuser Boston, Inc., Boston, MA, 1996. x+162 pp. (en)
- V.I. Bogachev. Measure theory. Vol. I. Springer-Verlag, Berlin, 2007. xviii+500 pp. (en)
- Lawrence C. Evans. Weak convergence methods for nonlinear partial differential equations. CBMS Regional Conference Series in Mathematics, 74. Published for the Conference Board of the Mathematical Sciences, Washington, DC; by the American Mathematical Society, Providence, RI, 1990. viii+80 pp. (en)
- P.L. Lions. The concentration-compactness principle in the calculus of variations. The limit case. I. Rev. Mat. Iberoamericana 1 , no. 1, 145–201. (en)
- Haïm Brézis and Elliott Lieb. A relation between pointwise convergence of functions and convergence of functionals. Proc. Amer. Math. Soc. 88 , no. 3, 486–490. (en)
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| 3loc
| - Lemma 1.32 (en)
- Theorem 1.9 (en)
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| 1a
| - Lions (en)
- Lieb (en)
- Brézis (en)
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| 1loc
| - Theorem 1 (en)
- Theorem 2 (en)
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| 3a
| - Lieb (en)
- Loss (en)
- Willem (en)
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| 2loc
| - Proposition 4.7.30 (en)
- Theorem 1.8 (en)
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| - In the mathematical field of analysis, the Brezis–Lieb lemma is a basic result in measure theory. It is named for Haïm Brézis and Elliott Lieb, who discovered it in 1983. The lemma can be viewed as an improvement, in certain settings, of Fatou's lemma to an equality. As such, it has been useful for the study of many variational problems. (en)
- У математичному аналізі лема Брезіса–Лієба є основним результатом в теорії міри. Вона названа на честь та , які довели її в 1983 році. Лему можна розглядати за певних умов як покращення леми Фату до рівності. Вона була корисна при дослідженні багатьох варіаційних проблем. (uk)
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