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 Mar 8 awarded Favorite Question May 25 awarded Famous Question Feb 23 awarded Good Question Jan 23 accepted Are Carnot groups (as Carnot Caratheodory metric spaces) doubling? Jan 23 asked Are Carnot groups (as Carnot Caratheodory metric spaces) doubling? Jan 18 accepted What are Carnot groups? Jan 18 comment What are Carnot groups? Yes thanks. That's what I was looking for. Jan 18 comment What are Carnot groups? I guess I need an introductory reference with a bunch of examples. Jan 18 asked What are Carnot groups? Sep 9 awarded Nice Answer Jul 2 awarded Curious Mar 1 asked Finding the lift of a curve under some assumptions Feb 26 awarded Notable Question Jan 21 accepted Is the speed of a curve in $\ell^\infty$ zero a.e. if the derivative of each component is zero a.e.? Jan 21 comment Is the speed of a curve in $\ell^\infty$ zero a.e. if the derivative of each component is zero a.e.? Thanks again. Yeah, you're absolutely right. Jan 20 comment Is the speed of a curve in $\ell^\infty$ zero a.e. if the derivative of each component is zero a.e.? Ok, so I think there might be a small problem with your argument. The problem is when you extend $f$ to the entire set of $\mathbb{R}$, let's call this extension $F$, then $F(t+h)$ is not necessarily equal to $f(t+h)$ because $t+h$ is not in $A$ necessarily. Hence, the estimate $\frac{\vert f(t+h)-f(t)\vert}{\vert h \vert} \leq 2L\epsilon$ doesn't hold. Am I missing something here possibly? Jan 18 comment Is the speed of a curve in $\ell^\infty$ zero a.e. if the derivative of each component is zero a.e.? And yes, $\mathcal{H}^1$ is just the 1-dimensional Hausdorff measure on $\mathbb{R}$ which coincides with the Lebesuge measure on $\mathbb{R}$. Jan 18 comment Is the speed of a curve in $\ell^\infty$ zero a.e. if the derivative of each component is zero a.e.? Thanks Nik. I just have a quick question. How did you conclude that $\frac{\vert f(t+h) - f(t) \vert}{\vert h \vert} \leq L\epsilon$ for all $\vert h \vert \leq r$? Jan 18 revised Is the speed of a curve in $\ell^\infty$ zero a.e. if the derivative of each component is zero a.e.? added 174 characters in body; edited title Jan 18 asked Is the speed of a curve in $\ell^\infty$ zero a.e. if the derivative of each component is zero a.e.?