The space $D$ in several variables: random variables and higher moments

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.

SUPPORT MANAGEMENT DECISIONS UNDER CONTROL OF TECHNICAL CONDITION OF RADIO-ELECTRONIC SYSTEMS OF RESPONSIBLE ASSIGNMENT

The article discusses the tasks of formation and selection to support management decisions when monitoring the technical condition of radio electronic systems. Responsible systems require more accurate estimates, which are obtained from all available information, including the behavior of parameters in the tolerance field. The model of the technological control system of the responsible-purpose system, the organizational-technological model of the technological control system control for the organization of the intelligent decision-making support system are given. The composition of parameters, criteria, constraints and mathematical models of optimization are given. A multi-criteria model of support for management decisions is presented in general form and interpreted as a utility function. Representing this function in a multilinear form makes it possible to take into account the specifics of the process and apply additive and multiplicative functions. The presented optimization models are the basis for creating databases, knowledge bases and the necessary operational rules to support management decisions.

Norm Attaining Arens Extensions onℓ1

We study norm attaining properties of the Arens extensions of multilinear forms defined on Banach spaces. Among other related results, we construct a multilinear form onℓ1with the property that only some fixed Arens extensions determined a priori attain their norms. We also study when multilinear forms can be approximated by ones with the property that only some of their Arens extensions attain their norms.

Estimates for a multilinear form on the sphere

The object of this paper is to make Lp estimates for the n-linear formdefined on n-tuples of functions (ø1, …, øn) on the sphere Sn−1 inℝn.