On weak convergence implying strong convergence under extremal conditions (Q1191845)
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scientific article; zbMATH DE number 62872
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | On weak convergence implying strong convergence under extremal conditions |
scientific article; zbMATH DE number 62872 |
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On weak convergence implying strong convergence under extremal conditions (English)
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27 September 1992
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\textit{T. Rzeżuchowski} [Bull. Aust. Math. Soc. 39, No. 2, 201-214 (1989; Zbl 0651.28007)] showed that under a certain extremal subset condition the weak convergence in an \(L^ 1\)-space does imply the strong one. The author has improved upon and extended Rzeżuchowski's result to the infinite-dimensional case by utilizing the theory of Young measures. His theorem also yields the main result of [same author, ibid. 33, 363-368 (1986; Zbl 0579.46018)].
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strong convergence
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extremal subset condition
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weak convergence
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\(L^ 1\)-space
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Young measures
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