Geodesic
Convergence of types under monotonous mappings
Teoriâ veroâtnostej i ee primeneniâ, Tome 38 (1993) no. 3, pp. 679-684

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Let $\mathcal F$ be the set of all D.F. on $\overline{\mathbf R}{}^d=[-\infty,\infty)^d$. Denote by $GMA$ the group of all max-automorphisms of $\overline{\mathbf R}{}^d$, i.e. such one-to-one mappings $L$ that preserve the max-operation in $\overline{\mathbf R}{}^d$, $L(x\vee y)=L(x)\vee L(y)$. We define type $(F):=\{G\in\mathscr{F}:\exists T\in GMA,G=F\circ T\}$. Hеге the convergence to type theorem is proved for distributions in $\mathcal F$ and norming sequences $\{L_n\}$ in $GMA$.
Keywords: extreme values, max-automorphisms.
Mots-clés : Convergence of types 
@article{TVP_1993_38_3_a21,
     author = {E. Pancheva},
     title = {Convergence of types under monotonous mappings},
     journal = {Teori\^a vero\^atnostej i ee primeneni\^a},
     pages = {679--684},
     publisher = {mathdoc},
     volume = {38},
     number = {3},
     year = {1993},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/TVP_1993_38_3_a21/}
}
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E. Pancheva. Convergence of types under monotonous mappings. Teoriâ veroâtnostej i ee primeneniâ, Tome 38 (1993) no. 3, pp. 679-684. http://geodesic.mathdoc.fr/item/TVP_1993_38_3_a21/