Timeline for A measure theory question

6 events

when toggle format	what		by	license	comment
Apr 5, 2012 at 11:09	comment	added	juan		Yes, the constant $e$ is only to make $x \log(e/x)$ monotone on $[0,1]$. In fact $H_f = H_g$ if $f$ and $g$ coincide on an interval $[0,\varepsilon]$, therefore there is some liberty in choosing $f$.
Apr 3, 2012 at 19:54	comment	added	Olga		Thank you so much for your answer, as far as I understand, for $\mathbb{R}^n$ we have to consider $f_n(x)=x^n \log (e/x)$ and everything will work as it has to. And the number e in the definition of f doesn't value much - we can take any positive number we want.
Apr 3, 2012 at 15:59	vote	accept	Olga
Apr 3, 2012 at 15:59	vote	accept	Olga
Apr 3, 2012 at 15:59
Mar 29, 2012 at 19:49	comment	added	juan		Perhaps I must explain that the existence of $A\subset{\bf R}$ with $0<H_f(A)<1$ is well known and due to Dvoretzky: Dvoretzky, A. A note on Hausdorff dimension functions. Proc. Cambridge Philos. Soc. 44, (1948). 13–16.
Mar 29, 2012 at 11:30	history	answered	juan	CC BY-SA 3.0