Abstract
In this chapter we establish a lower bound for the dimension of the convex set of faithful invariant states in every finitely presented MV-algebra, and we give a purely MV-algebraic generalization of the Lebesgue integral of McNaughton functions on rational polyhedra. Since every faithful state of an MV-algebra
Keywords
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
This is a preview of subscription content, log in via an institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsReferences
Marra, V., Mundici, D. (2007). The Lebesgue state of a unital abelian \({\ell}\)-group. Journal of Group Theory, 10, 655–684.
Marra, V. (2009). The Lebesgue state of a unital abelian lattice-ordered group II. Journal of Group Theory, 12, 911–922.
Panti, G., (2008). Invariant measures in free MV-algebras. Communications in Algebra, 36, 2849–2861.
Leustean, I. (2011). Metric Completions of MV-algebras with States: An Approach to Stochastic Independence. Journal of Logic and Computation, 21(3), 493–508.
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
Copyright information
© 2011 Springer Science+Business Media B.V.
About this chapter
Cite this chapter
Mundici, D. (2011). The Lebesgue State and the Completion of \({\mathsf {FREE}}_n\) . In: Advanced Łukasiewicz calculus and MV-algebras. Trends in Logic, vol 35. Springer, Dordrecht. https://doi.org/10.1007/978-94-007-0840-2_16
Download citation
DOI: https://doi.org/10.1007/978-94-007-0840-2_16
Published:
Publisher Name: Springer, Dordrecht
Print ISBN: 978-94-007-0839-6
Online ISBN: 978-94-007-0840-2
eBook Packages: Mathematics and StatisticsMathematics and Statistics (R0)