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Modular measures and Maharam operators. (Russian) Zbl 1030.47027
Summary: The aim of this paper is to show that modular measures and Maharam operators are closely related to each other. Namely, integration over a saturated measure produces a Maharam operator and an integral representation of a Maharam operator gives rise to a modular saturated pair.
MSC:
47B60 Linear operators on ordered spaces
46A40 Ordered topological linear spaces, vector lattices
47B40 Spectral operators, decomposable operators, well-bounded operators, etc.
46E40 Spaces of vector- and operator-valued functions
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