Set-valued integration in seminorm. I

The purpose of this paper is to define an integral for multifunctions with respect to an additive multimeasure. If P-k (X) is the family of nonempty compact subsets of a locally convex algebra X, then both the multifunction and the multimeasure take values in a subset (X) over tilde of P-k (X) which satisfies certain conditions. This integral is weaker than that introduced in Croitoru [6] and contains, as particular cases, the integrals defined in Sambucini [11] and Croitoru [5]. The method used for integration is an extension of that introduced by Blondia [1].