User ema - MathOverflow most recent 30 from http://mathoverflow.net 2013-05-23T06:01:01Z http://mathoverflow.net/feeds/user/19290 http://www.creativecommons.org/licenses/by-nc/2.5/rdf http://mathoverflow.net/questions/81778/homogenuity-of-ellp homogenuity of $\ell^p$ Ema 2011-11-24T05:41:20Z 2011-11-24T14:15:58Z <p>I want to know the following:</p> <p>If $x_1, x_2, \cdots, x_n, y_1,y_2, \cdots, y_n \in \ell_p$ satisfies $\|x_i-x_j\|_p=\|y_i-y_j\|_p$ for any $i,j$, then does there exist isometry $F$ of $\ell_p$ which send each $x_i$ to $y_i$ ?</p> <p>Also do you know the precise description of the isometry group of $\ell_p$ ?</p> http://mathoverflow.net/questions/80986/question-on-geometric-measure-theory Question on geometric measure theory Ema 2011-11-15T14:39:23Z 2011-11-15T17:54:07Z <p>I want to know the following is well-known or not:</p> <p>Let X be a metric space with Hausdorff dimension $\alpha$. Then for any $\beta &lt; \alpha$, X contains a closed subset whose Hausdorff dimension is $\beta$.</p> http://mathoverflow.net/questions/81778/homogenuity-of-ellp/81808#81808 Comment by Ema Ema 2011-12-14T18:23:00Z 2011-12-14T18:23:00Z &gt;Edger thanks! http://mathoverflow.net/questions/81778/homogenuity-of-ellp/81783#81783 Comment by Ema Ema 2011-12-14T18:22:17Z 2011-12-14T18:22:17Z &gt;Alain Valette Thank you very much! Thanks to you, I understand precisely. http://mathoverflow.net/questions/80986/question-on-geometric-measure-theory/80987#80987 Comment by Ema Ema 2011-11-18T16:47:52Z 2011-11-18T16:47:52Z Thank you very much for many information! http://mathoverflow.net/questions/80986/question-on-geometric-measure-theory/80987#80987 Comment by Ema Ema 2011-11-15T18:03:41Z 2011-11-15T18:03:41Z Thank you very much. I do not know where you use the finitness assumption of \alpha in your argument. The finiteness seems to be needed only for \beta. If it is possible, would you please tell me which statement you used in Howroyd's paper?