On The Integral Representation of Strictly Continuous Set-Valued Maps

On The Integral Representation of Strictly Continuous Set-Valued Maps

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Let T be a completely regular topological space and C(T) be the space of bounded, continuous real-valued functions on T.C(T) is endowed with the strict Garden topology (the topology generated by seminorms determined by continuous functions vanishing at in_nity).R.Giles ([13], p.

472, Theorem 4.6) proved in 1971 that the dual of C(T) can be identi_ed with the space of regular Borel measures on T.We prove this Dental Cement result for positive, additive set-valued maps with values in the space of convex weakly compact non-empty subsets of a Banach space and we deduce from this result the theorem of R.Giles ([13], theorem 4.

6, p.473).