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).
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References
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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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