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

被引：4

作者：

Avallone, Anna ^{[1
]}

Vitolo, Paolo ^{[1
]}

机构：

[1] Univ Basilicata, Dipartimento Matemat & Informat, I-85100 Potenza, Italy

来源：

ACTA MATHEMATICA SCIENTIA | 2013年 / 33卷 / 03期

关键词：

Pseudo-effect algebra; pseudo-D-lattice; D-uniformity; lattice uniformity; modular measure; CONTINUOUS SET-FUNCTIONS; TOPOLOGICAL RINGS; UNIFORM LATTICES; CENTRAL ELEMENTS; ALGEBRAS;

D O I：

10.1016/S0252-9602(13)60028-4

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

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.

引用

页码：653 / 677

页数：25

共 17 条

[1] LEBESGUE DECOMPOSITION AND BARTLE-DUNFORD-SCHWARTZ THEOREM IN PSEUDO-D-LATTICES
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ActaMathematicaScientia, 2013, 33 (03) : 653 - 677
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