Geodesic
Strong laws for~sums of~extreme values
Teoriâ veroâtnostej i ee primeneniâ, Tome 42 (1997) no. 3, pp. 553-563

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We present a new approach to strong laws for sums of extreme values of sequences of independent not necessarily identically distributed random variables. Our technique is based on a simple extension of an inequality of M. Marcus and G. Pisier [M. Marcus and G. Pisier, Acta Math., 152 (1984), pp. 245–301.] on the tail distribution of weak $l_p$ norms of independent sequences of real random variables. Our results are also related to some extensions of the Marcinkiewicz–Zygmund law of large numbers.
Keywords: order statistics, extreme values, laws of largenumbers, Marcinkiewicz–Zygmund law of large numbers, Banach spaces. 
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     author = {M. Broniatowski and M. Weber},
     title = {Strong laws for~sums of~extreme values},
     journal = {Teori\^a vero\^atnostej i ee primeneni\^a},
     pages = {553--563},
     publisher = {mathdoc},
     volume = {42},
     number = {3},
     year = {1997},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/TVP_1997_42_3_a6/}
}
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M. Broniatowski; M. Weber. Strong laws for~sums of~extreme values. Teoriâ veroâtnostej i ee primeneniâ, Tome 42 (1997) no. 3, pp. 553-563. http://geodesic.mathdoc.fr/item/TVP_1997_42_3_a6/