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age 27
visits member for 5 years, 3 months
seen Apr 1 at 18:37

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.?
Jan
7
awarded  Notable Question
Nov
10
comment Hausdorff measure and projections
Thank you, Pietro.