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

doi:10.1016/S0252-9602(13)60028-4

Abstract

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.

Key words: Pseudo-effect algebra, pseudo-D-lattice, D-uniformity, lattice uniformity, mod-ular measure

CLC Number:

28B10

Anna AVALLONE, Paolo VITOLO. LEBESGUE DECOMPOSITION AND BARTLE–DUNFORD–SCHWARTZ THEOREM IN PSEUDO-D-LATTICES[J].Acta mathematica scientia,Series B, 2013, 33(3): 653-677.

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