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Isolated and antiisolated measures

General Measure Theory

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Part of the Lecture Notes in Mathematics book series (LNM,volume 1089)

Abstract

Given a band M of the complete vector lattice M(R) of real-valued measures on a δ-ring R, the notions of M-isolated and M-antiisolated measures are introduced. If M is the set of Radon measures on a Hausdorff space, the set Mis of ℓ-isolated measures coincides with the set of atomical ones, and the set Mant of M-antiisolated measures with the set of atomfree ones, but in the general case this is not true. Via representations of spaces of measures another characterization of the elements of Mis and Mant is given, and it is proved that M=Mis ⊕ Mant (in the sense of vector lattices).

Keywords

  • Vector Lattice
  • Radon Measure
  • Hausdorff Space
  • Riesz Space
  • Atomical Measure

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References

  1. C. Constantinescu, Duality in Measure Theory, Springer-Verlag, New York-Heidelberg-Berlin (1980).

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  2. W.A.J. Luxemburg and A.C. Zaanen, Riesz Spaces I, North-Holland Publishing Company, Amsterdam-London (1971).

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  3. T. Traynor, Decomposition of group-valued additive set functions, Ann. Inst. Fourier, Grenoble, 22, 3 (1972), 131–140.

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© 1984 Springer-Verlag

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Filter, W. (1984). Isolated and antiisolated measures. In: Kölzow, D., Maharam-Stone, D. (eds) Measure Theory Oberwolfach 1983. Lecture Notes in Mathematics, vol 1089. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0072596

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  • DOI: https://doi.org/10.1007/BFb0072596

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-13874-7

  • Online ISBN: 978-3-540-39069-5

  • eBook Packages: Springer Book Archive