bio | website | |
---|---|---|
location | ||
age | 27 | |
visits | member for | 5 years |
seen | 5 hours ago | |
stats | profile views | 529 |
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. |
Nov 10 |
comment |
Hausdorff measure and projections
The standard metric on $ \ell^\infty $ which is the supremum metric. And you're right. I should've been more careful about the projections. I meant to say projection onto the first m components. $ \pi_V(x_1, x_2, \dots) = (x_1, \dots, x_m) $. |