论文标题
在欧几里得拓扑的Hausdorff量子
On the Hausdorff Measure of $\R^n$ with the Euclidean Topology
论文作者
论文摘要
在本文中，我们回答了大卫·H·弗里姆林（David H.特别是，我们证明，当考虑诱导欧几里得拓扑的距离时，$ \ mathbb {r}^n $的Hausdorff $ n $维度度量绝不是$ 0 $。最后，我们通过反例表明，如果我们删除对拓扑的假设，则先前的结果一般不会得出。
In this paper we answer a question raised by David H. Fremlin about the Hausdorff measure of $\mathbb{R}^2$ with respect to a distance inducing the Euclidean topology. In particular we prove that the Hausdorff $n$-dimensional measure of $\mathbb{R}^n$ is never $0$ when considering a distance inducing the Euclidean topology. Finally, we show via counterexamples that the previous result does not hold in general if we remove the assumption on the topology.
