I was doing some reading and I came across this:(adsbygoogle = window.adsbygoogle || []).push({});

http://en.wikipedia.org/wiki/Total_variation_distance_of_probability_measures

So apparently for the finite case,

[tex]\max_{x} ( \left| P(x) - Q(x) \right|)\quad \mbox{ is equivalent to}\quad \frac{1}{2} \sum_x {\left| P(x)-Q(x)\right|}[/tex]

but isn't this is a counterexample?

sum(|P-Q|)/2= 0.2Code (Text):

x 1 2 3 4

P(x) 0.25 0.25 0.25 0.25

Q(x) 0.10 0.20 0.35 0.35

|P-Q| 0.15 0.05 0.10 0.10

max(|P-Q|)=0.15

So I was thinking, maybe they meant 'equivalent' in a different sense? Could somebody please explain?

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# Variation distance?

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