In this paper, we answer a question raised by David H. Fremlin about the Hausdorff measure of R2 with respect to a distance inducing the Euclidean topology. In particular we prove that the Hausdorff n-dimensional measure of Rn 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.

On the Hausdorff Measure of Rn with the Euclidean Topology

Bagnara, Marco
;
Luongo Eliseo
2023

Abstract

In this paper, we answer a question raised by David H. Fremlin about the Hausdorff measure of R2 with respect to a distance inducing the Euclidean topology. In particular we prove that the Hausdorff n-dimensional measure of Rn 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.
2023
Settore MAT/05 - Analisi Matematica
Hausdorff measure, Euclidean topology
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11384/142285
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