A Relation Between Pointwise Convergence of Functions and Convergence of Functionals
A Relation Between Pointwise Convergence of Functions and Convergence of Functionals
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DOI：
10.1007/978-3-642-55925-9_42
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发表时间：
1983-03
期刊：
影响因子：
--
通讯作者：
H. Brezis;E. Lieb
中科院分区：
文献类型：
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作者：
H. Brezis;E. Lieb
我们证明了IF是度量空间上一致有界的函数序列，如果是逐点的，则对所有函数都是一致有界的。这一结果也在定理2中推广到除泛函外的某些泛函，即适用于和适用于一个序列。简要讨论了这一结果在变分问题中的应用。参考文献
We show that ifis a sequence of uniformly-bounded functions on a measure space, and ifpointwise ae, thenfor all. This result is also generalized in Theorem 2 to some functionals other than thenorm, namelyfor suitableand a suitable sequence. A brief discussion is given of the usefulness of this result in variational problems. References