LEBESGUE DECOMPOSITION AND BARTLE-DUNFORD-SCHWARTZ THEOREM IN PSEUDO-D-LATTICES
LEBESGUE DECOMPOSITION AND BARTLE-DUNFORD-SCHWARTZ THEOREM IN PSEUDO-D-LATTICES
摘要
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.
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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