The integral representation of vector measures on a completely regular space

We consider the vector space C(X, E) of all bounded continuous functions from a completely regular space X into a Banach space E. It is given a special locally convex topology . We prove the analog of the Riesz-Markov theorem for the -continuous linear operators which map C (X, E) into a Banach space F.Translated from Matematicheskie Zametki, Vol. 20, No. 3, pp. 401–408, September, 1976.