Abstract
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.
Citation
Marco Bagnara. Luca Gennaioli. Giacomo Maria Leccese. Eliseo Luongo. "On the Hausdorff Measure of $\mathbb{R}^n$ with the Euclidean Topology." Real Anal. Exchange 48 (1) 101 - 106, 2023. https://doi.org/10.14321/realanalexch.48.1.1649735306
Information