TY - JOUR
AU - Janson, Svante
PY - 2021/11/30
Y2 - 2022/01/22
TI - The space $D$ in several variables: random variables and higher moments
JF - MATHEMATICA SCANDINAVICA
JA - Math. Scand.
VL - 127
IS - 3
SE - Articles
DO - 10.7146/math.scand.a-128971
UR - https://www.mscand.dk/article/view/128971
SP -
AB - <p>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 $\sigma$-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.</p>
ER -