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Continuous linear functionals on the space of Borel vector measures

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Siwek P.

Annales Polonici Mathematici

2008

tom 93

nr 3

199-209

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 $||·||_{ℱ}$ 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 $(ℳ,||·||_{ℱ})*$ is contained in but not equal to the space (ℳ,||·||(X))*. We obtain a representation of the continuous functionals on ℳ in some particular cases.

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1 Annales Polonici Mathematici

1 Siwek P.

1 2008

Wyniki wyszukiwania

Continuous linear functionals on the space of Borel vector measures