论文标题
部分可观测时空混沌系统的无模型预测
A note on the Schur and Phillips lemmas
论文作者
论文摘要
众所周知，$ \ ell_1 $中的每个弱收敛序列都在规范拓扑（Schur的引理）中收敛。 Phillips' lemma asserts even more strongly that if a sequence $(μ_n)_{n\in\mathbb N}$ in $\ell_\infty'$ converges pointwise on $\{0,1\}^\mathbb N$ to $0$, then its $\ell_1$-projection converges in norm to $0$.在本说明中，我们展示了Schur的引理的第二类版本如何使用简短的证明，可用于替换Phillips的引理$ \ \ {0,1 \}^\ Mathbb n $，其中包含所有有限设置的任何子集，并为有限设置提供某种插入属性。
It is well-known that every weakly convergent sequence in $\ell_1$ is convergent in the norm topology (Schur's lemma). Phillips' lemma asserts even more strongly that if a sequence $(μ_n)_{n\in\mathbb N}$ in $\ell_\infty'$ converges pointwise on $\{0,1\}^\mathbb N$ to $0$, then its $\ell_1$-projection converges in norm to $0$. In this note we show how the second category version of Schur's lemma, for which a short proof is included, can be used to replace in Phillips' lemma $\{0,1\}^\mathbb N$ by any of its subsets which contains all finite sets and having some kind of interpolation property for finite sets.
