Аннотация:
We study the convergence of triangular mappings on ${\mathbb R}^n,$ i.e., mappings $T$ such that
the $i$th coordinate function $T_i$ depends only on the variables $x_1,\ldots,x_i.$ Weshow
that, under broad assumptions, the inverse mapping to a canonical triangular transformation is canonical triangular as well. An example is constructed showing that
the convergence in variation of measures is not sufficient for the convergence almost
everywhere of the associated canonical triangular transformations. Finally, we show
that the weak convergence of absolutely continuous convex measures to an absolutely
continuous measure yields the convergence in variation. As a corollary, this implies
the convergence in measure of the associated canonical triangular transformations.
Ключевые слова:
Triangular transformations, weak convergence of measures, convex measures.
Полный текст:
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