Nonstandard discretization and the Loeb extension of a family of measures

The first part of the article deals with discretization of an integral operator by means of nonstandard analysis. Any integral operator is proved to be approximable to within infinitesimal by a matrix of infinite size. In the second part, the Loeb construction for a random measure is implemented and a connection of the construction with vector Loeb measures and nonstandard hulls is studied.