Let L be a lattice ordered effect algebra. We prove that the lattice uniformities on L which makes ⊖ and ⊕ uniformly continuous form a Boolean algebra isomorphic to the centre of a suitable complete effect algebra 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

Decomposition and control theorems in effect algebras

AVALLONE, Anna;VITOLO, Paolo
2003

Abstract

Let L be a lattice ordered effect algebra. We prove that the lattice uniformities on L which makes ⊖ and ⊕ uniformly continuous form a Boolean algebra isomorphic to the centre of a suitable complete effect algebra 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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Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/11563/17343
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