# VC dimension and epsilon-nets

• Jun 28th 2012, 06:13 AM
aharonidan
VC dimension and epsilon-nets
Hey math experts, I need a little help with a proof.
I found a sketch of the proof I want to do on the web(attached) , and I find it difficult to understand.

Attachment 24183

1. The definition of $E$. (I spouse there is a mistake there and it should be $E:=${{ $l \in L$ : $l \cap e \not= \emptyset$ } : $e$ is segment}) what do they mean by "e is a segment"?

2. What is the explanation to the existence of such a " $2/3r$-net" of $\Sigma$?

3. Why does the fact that R is a $2/3r$-net means that each triangle does not intersect more than $n/r$ lines?

Any help will be appreciated.