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

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

数学物理学报(英文版) ›› 2013, Vol. 33 ›› Issue (3): 653-677.doi: 10.1016/S0252-9602(13)60028-4

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

Anna AVALLONE|Paolo VITOLO

Dipartimento di Matematica e Informatica, Universit`a della Basilicata, Viale dell’Ateneo Lucano 10, 85100 Potenza, Italy

收稿日期:2011-11-17 出版日期:2013-05-20 发布日期:2013-05-20

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

Anna AVALLONE|Paolo VITOLO

Dipartimento di Matematica e Informatica, Universit`a della Basilicata, Viale dell’Ateneo Lucano 10, 85100 Potenza, Italy

Received:2011-11-17 Online:2013-05-20 Published:2013-05-20

摘要/Abstract

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.

关键词: Pseudo-effect algebra, pseudo-D-lattice, D-uniformity, lattice uniformity, mod-ular measure

Abstract:

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

中图分类号:

28B10

Anna AVALLONE, Paolo VITOLO. LEBESGUE DECOMPOSITION AND BARTLE–DUNFORD–SCHWARTZ THEOREM IN PSEUDO-D-LATTICES[J]. 数学物理学报(英文版), 2013, 33(3): 653-677.

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

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

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