LFD Book Forum Discussion of the VC proof
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10-26-2016, 02:28 PM
 CountVonCount Member Join Date: Oct 2016 Posts: 17
Re: Discussion of the VC proof

I have also another question on the same page (190):
At the end of the page there is the formula:

$\sum_S&space;\mathbb{P}[S]\times\mathbb{P}[sup_{h\in&space;H}\vert&space;E_{in}(h)&space;-&space;{E_{in}}'(h))&space;\vert&space;>&space;\frac{\varepsilon&space;}{2}]&space;\leq&space;sup_S&space;\mathbb{P}[sup_{h\in&space;H}\vert&space;E_{in}(h)&space;-&space;{E_{in}}'(h))&space;\vert&space;>&space;\frac{\varepsilon&space;}{2}]&space;\vert&space;S&space;]$

I don't understand why the RHS is greater or equal to the LHS. The only legitimation I see for this is, that the distribution of P[S] is uniform, but this has not been stated in the text.
Or do I oversee here anything and this is also valid for all kinds of distribution?

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