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

J. Math. Sci. Univ. Tokyo
Vol. 3 (1996), No. 3, Page 533--546.

Precupanu, Anca-Maria
A Brooks Type Integral with Respect to a Set-Valued Measure
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Abstract:
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.

Mathematics Subject Classification (1991): Primary 28B20; Secondary 28A25, 28B10
Mathematical Reviews Number: MR1432107

Received: 1995-04-12