论文标题
公制空间的无lipschitz空间，超副作用和有限的表示
Lipschitz-free spaces, ultraproducts, and finite representability of metric spaces
论文作者
论文摘要
我们研究了公制空间$ m $的超能$ m _ {\ mathcal u} $的几个属性和应用。我们证明，无LIPSCHITZ的空间$ \ MATHCAL F（M _ {\ MATHCAL U}）$在$ \ Mathcal f（m）$中有限表示。我们还表征了在Banach空间中代表有限的Lipschitz的度量空间，就像Bilipschitz嵌入Banach空间的超人中的度量空间。多亏了此链接，我们得到的是，如果$ m $在banach space $ x $中代表有限的Lipschitz，则$ \ Mathcal f（m）$在$ \ Mathcal f（x）$中有限表示。我们将这些结果应用于无Lipschitz空间中的Cotype以及Lipschitz的空间和Lipschitz功能的稳定性。
We study several properties and applications of the ultrapower $M_{\mathcal U}$ of a metric space $M$. We prove that the Lipschitz-free space $\mathcal F(M_{\mathcal U})$ is finitely representable in $\mathcal F(M)$. We also characterize the metric spaces that are finitely Lipschitz representable in a Banach space as those that biLipschitz embed into an ultrapower of the Banach space. Thanks to this link, we obtain that if $M$ is finitely Lipschitz representable in a Banach space $X$, then $\mathcal F(M)$ is finitely representable in $\mathcal F(X)$. We apply these results to the study of cotype in Lipschitz-free spaces and the stability of Lipschitz-free spaces and spaces of Lipschitz functions under ultraproducts.
