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 : :&nbsp;Cai-Yun Ma,&nbsp;Yu-Feng Wu</p> <p>Abstract : We prove that for all s&isin;(0,d) and c&isin;(0,1) there exists a self-similar set E&sub;Rd with Hausdorff dimension s such that Hs(E)=c|E|s. This answers a question raised by Zhiying Wen</p> <p><a href="https://medium.com/@monocosmo77/making-machine-learning-pipelines-with-hausdorff-measure-part4-b540e3cf0739">Visit Now</a></p>