As the title says.
Let $A^n$ be an $n$-dimensional closed Alexandrov space. Does it admit a bi-Lipschitz embedding into Euclidean space $\mathbb R^N$ for sufficiently large $N$?


I know there are some spaces that do not admit such an embedding; for example, a theorem by Pansu says that: 



> 
> The Heisenberg group
>  equipped with the Carnot-Caratheodory distance does not biLipschitz embed into $\mathbb R^n$,
>  for any $n$.
> 
> 
> 



Does closed Alexandrov space admit a bi-Lipschitz embedding into $\mathbb R^N$?
See Distance embedding (27.5) in [our book](http://dl.dropboxusercontent.com/u/1577084/the-book.pdf)


