Making Machine Learning pipelines with Hausdorff Measure part4
<p>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</p>
<p>2.A note on Hausdorff measures of self-similar sets in Rd (arXiv)</p>
<p>Author : : Cai-Yun Ma, Yu-Feng Wu</p>
<p>Abstract : We prove that for all s∈(0,d) and c∈(0,1) there exists a self-similar set E⊂Rd with Hausdorff dimension s such that Hs(E)=c|E|s. This answers a question raised by Zhiying Wen</p>
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