论文标题
几个变量中的空间$ d $：随机变量和较高的矩
The space $D$ in several variables: random variables and higher moments
论文作者
论文摘要
我们研究了几个变量的banach space $ d（[0,1]^m）$（从某种意义上说）右连续的几个变量，并扩展了标准情况$ M = 1 $的几个结果。例如，我们给出了双重空间的描述，并且我们表明，相对于点评估生成的$σ$字段总是可以衡量的。这些结果用于研究该空间中的随机功能。 （即，空间的随机元素。）特别是，我们给出了这种随机函数的矩（不同意义上）的结果，并给出了两个这样的随机函数之间的Zolotarev距离。
We study the Banach space $D([0,1]^m)$ of functions of several variables that are (in a certain sense) right-continuous with left limits, and extend several results previously known for the standard case $m=1$. We give, for example, a description of the dual space, and we show that a bounded multilinear form always is measurable with respect to the $σ$-field generated by the point evaluations. These results are used to study random functions in the space. (I.e., random elements of the space.) In particular, we give results on existence of moments (in different senses) of such random functions, and we give an application to the Zolotarev distance between two such random functions.
