A Brooks Type Integral with Respect to a Set-Valued Measure

概要

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A generalization of the set--valued Brooks integral [3] with respect to a set--valued measure whose values are subsets of a Hausdorff locally convex topological vector space is presented. The construction of this new kind of integral is based on Weber's result [19] concerning the existence of a family of semi--invariant pseudo--metrics which ge\-ne\-ra\-tes the uniformity of a uniform semigroup (in our case, the semigroup of convex, bounded, closed subsets of a Hausdorff locally convex topological vector space). Several properties of the new integral are given and also a theorem of Vitali type is established.