The approximation theorem of convolution operator in △p set-valued function space

The paper is a contribution to the problem of approximating random set with values in a separable Banach space. This class of set-valued function is widely used in many areas. We investigate the properties of p-bounded integrable random set. Based on this we endow it with Ap metric which can be viewed as a integral type hausdorff metric and present some approximation theorem of a class of convolution operators with respect to △p metric. Moreover we also can establish analogous theorem for other integral type operator in △p space. © Springer-Verlag 2002.