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We study properties of the space ℳ of Borel vector measures on a compact metric space X, taking values in a Banach space E. The space ℳ is equipped with the Fortet-Mourier norm ${\left|\right|·\left|\right|}_{ℱ}$ and the semivariation norm ||·||(X). The integral introduced by K. Baron and A. Lasota plays the most important role in the paper. Investigating its properties one can prove that in most cases the space $(ℳ,|\left|·\right|{|}_{ℱ})*$ is contained in but not equal to the space (ℳ,||·||(X))*. We obtain a representation of the continuous functionals on...