论文标题
HAAR空凸组的拓扑表征
A Topological Characterisation of Haar Null Convex Sets
论文作者
论文摘要
在$ \ mathbb {r}^d $中，一个封闭的凸集集的lebesgue量度为零，并且只有其内部为空。更普遍的是，在可分离的，反射性的Banach空间中，封闭式和凸组是haar null的，并且仅当它们的内部为空时。我们通过表明在可分离的Banach空间中的封闭式凸面设置为HAAR NULL时，我们仅当其弱$^*$闭合在第二个双重的情况下，就规范拓扑具有空内部装置，因此扩展了这一事实。然后是，在所有非空的，封闭，凸和有限的子集的度量空间中，Haar Null集合的收敛序列具有HAAR无效限制。
In $\mathbb{R}^d$, a closed, convex set has zero Lebesgue measure if and only its interior is empty. More generally, in separable, reflexive Banach spaces, closed and convex sets are Haar null if and only if their interior is empty. We extend this facts by showing that a closed, convex set in a separable Banach space is Haar null if and only if its weak$^*$ closure in the second dual has empty interior with respect to the norm topology. It then follows that, in the metric space of all nonempty, closed, convex and bounded subsets of a separable Banach space, converging sequences of Haar null sets have Haar null limits.
