Stability of the ball-covering property
 作者： Zhenghua Luo,  Bentuo Zheng 作者单位： 1School of Mathematical Sciences Huaqiao University Quanzhou, Fujian, China, 3620212Department of Mathematical Sciences University of Memphis Memphis, TN 38120, U.S.A. 刊名： Studia Mathematica, 2020, Vol.250 , pp.19-34 来源数据库： Institute of Mathematics Polish Academy of Sciences DOI： 10.4064/sm180607-6-10 原始语种摘要： A normed space $X$ is said to have the ball-covering property (BCP,for short) if its unit sphere can be covered by the union of countablymany closed balls not containing the origin. Let $(\varOmega, \varSigma, \mu)$ bea separable measure space and $X$ be a normed space. We show that$L_p(\mu, X)$ $(1\leq p \lt \infty)$ has the BCP if and only if $X$ hasthe BCP. We also prove that if $\{X_k\}$ is a sequence of normedspaces, then ${\mathbf X}=(\sum\oplus X_k)_p$ has the BCP if andonly each $X_k$ has the BCP, where $1\leq p\leq\infty$. However, it isshown that $L_{\infty}[0, 1]$ fails the BCP.

• covering　覆盖物
• property　所有权
• separable　可分的
• where　哪里
• sphere
• covered　有盖的
• normed　赋范的
• short　短的
• measure　测度
• sequence　次序