Criteria for closedness of vector measures

Ricker, W.

doi:10.1090/S0002-9939-1984-0735568-X

Criteria for closedness of vector measures
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Proc. Amer. Math. Soc. 91 (1984), 75-80 Request permission

Abstract:

It is shown that there is a large class of locally convex spaces, which includes, for example, all spaces which are metrizable or Suslin or have the strict Mackey convergence property as well as many dual spaces, with the property that any vector measure assuming its values in such a space is a closed measure.

References

Nicolas Bourbaki, Éléments d’histoire des mathématiques, Histoire de la Pensée, No. IV, Hermann, Paris, 1974 (French). Nouvelle édition revue, corrigée et augmentée. MR 0349314
Cecilia H. Brook and William H. Graves, Closed measures, Proceedings of the Conference on Integration, Topology, and Geometry in Linear Spaces (Univ. North Carolina, Chapel Hill, N.C., 1979) Contemp. Math., vol. 2, Amer. Math. Soc., Providence, R.I., 1980, pp. 145–160. MR 621856
Klaus Floret, Weakly compact sets, Lecture Notes in Mathematics, vol. 801, Springer, Berlin, 1980. Lectures held at S.U.N.Y., Buffalo, in Spring 1978. MR 576235
Igor Kluvánek, The range of a vector-valued measure, Math. Systems Theory 7 (1973), 44–54. MR 322131, DOI 10.1007/BF01824806
Igor Kluvánek, Conical measures and vector measures, Ann. Inst. Fourier (Grenoble) 27 (1977), no. 1, v, 83–105 (English, with French summary). MR 470173

Vector measures and control systems

Topological vector spaces

W. Ricker, On Boolean algebras of projections and scalar-type spectral operators, Proc. Amer. Math. Soc. 87 (1983), no. 1, 73–77. MR 677235, DOI 10.1090/S0002-9939-1983-0677235-6
Elias Saab, On the Radon-Nikodým property in a class of locally convex spaces, Pacific J. Math. 75 (1978), no. 1, 281–291. MR 500045
G. Erik F. Thomas, Integration of functions with values in locally convex Suslin spaces, Trans. Amer. Math. Soc. 212 (1975), 61–81. MR 385067, DOI 10.1090/S0002-9947-1975-0385067-1
François Trèves, Topological vector spaces, distributions and kernels, Academic Press, New York-London, 1967. MR 0225131