, When P 1 = P (M 1 ?bm)/am is the distribution of the normalized block maxima and P 2 = G ? is the GEV distribution, we get V 1 (z) = (V (mz) ? V (m))/a(m)

, Since a is regularly varying with index ?, a(m) p e ?m/m 0 ? 0 as m ? ?. Letting m ? ?

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