Lebesgue decomposition and bartle—dunford—schwartz theorem in pseudo-D-lattices |
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Authors: | Anna AVALLONE Paolo VITOLO |
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Institution: | Dipartimento di Matematica e Informatica, Università della Basilicata, Viale dell''Ateneo Lucano 10, 85100 Potenza, Italy |
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Abstract: | Let L be a pseudo-D-lattice. We prove that the exhaustive lattice uniformities on L which makes the operations of L uniformly continuous form a Boolean algebra isomorphic to the centre of a suitable complete pseudo-D-lattice associated to L. As a consequence, we obtain decomposition theorems—such as Lebesgue and Hewitt—Yosida decompositions—and control theorems—such as Bartle—Dunford—Schwartz and Rybakov theorems—for modular measures on L. |
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Keywords: | Pseudo-effect algebra pseudo-D-lattice D-uniformity lattice uniformity modular measure |
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