论文标题
（最大的）lebesgue编号及其相对版本
The (largest) Lebesgue number and its relative version
论文作者
论文摘要
在本文中，我们比较了（最大）Lebesgue的不同定义，用于公制空间$ x $的封面$ \ mathcal {u} $。我们还介绍了Lebesgue的相对版本，用于子集$ a \ subseteq x $的涵盖家庭$ \ Mathcal {u} $，并通过给出校正的陈述和证明的相关性来证明与S.指标空间之间具有系数$ r $的同构图，以及在地图两侧的子集的网格和勒布斯格的比较。
In this paper we compare different definitions of the (largest) Lebesgue number of a cover $\mathcal{U}$ for a metric space $X$. We also introduce the relative version for the Lebesgue number of a covering family $\mathcal{U}$ for a subset $A\subseteq X$, and justify the relevance of introducing it by giving a corrected statement and proof of the Lemma 3.4 from S. Buyalo - N. Lebedeva paper "Dimensions of locally and asymptotically self-similar spaces", involving $λ$-quasi homothetic maps with coefficient $R$ between metric spaces, and the comparison of the mesh and the Lebesgue number of a covering family for a subset on both sides of the map.
