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ilson · #13 10-01-2015, 08:32 PM

I was going through the proof in Appendix A and I just want to make sure that something written towards the bottom of pg. 189 is a typo.

Namely,

Quote:

Inequality (A.3) folows because the events " $|E'_{in}(h^*)-E_{out}(h^*)|\leq \frac{\epsilon}{2}$ " and " $|E_{in}(h^*)-E_{out}(h^*)|>\epsilon$ " (which is given) imply " $|E_{in}(h)-E'_{in}(h)|>\frac{\epsilon}{2}$ ".

should read

Quote:

Inequality (A.3) folows because the events " $|E'_{in}(h^*)-E_{out}(h^*)|\leq \frac{\epsilon}{2}$ " and " $|E_{in}(h^*)-E_{out}(h^*)|>\epsilon$ " (which is given) imply " $|E_{in}(h^*)-E'_{in}(h^*)|>\frac{\epsilon}{2}$ ".

I'm 99.999999999999% sure this is indeed a typo since the latter case easily follows from reverse triangle inequality and it suffices to show the inequality in (A.3) and I cannot see how one can arrive at the implication in the former case nor how the former case implies the inequality (A.3), but it would ease my mind if I can get a verification that it is a typo. Thank you in advance!