Various combinatorial equivalents are given to the Lebesgue state in archimedean lattice-ordered groups with order-unit. The proofs use piecewise linear functions on polyhedra with rational vertices.
The Lebesgue state of a unital abelian lattice-ordered group / D.MUNDICI; V. MARRA. - In: JOURNAL OF GROUP THEORY. - ISSN 1433-5883. - STAMPA. - 10:(2007), pp. 655-684. [10.1515/JGT.2007.049]
The Lebesgue state of a unital abelian lattice-ordered group
MUNDICI, DANIELE;
2007
Abstract
Various combinatorial equivalents are given to the Lebesgue state in archimedean lattice-ordered groups with order-unit. The proofs use piecewise linear functions on polyhedra with rational vertices.
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