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\iteman{io-port 06110880}
\itemau{Leu\c{s}tean, Ioana}
\itemti{State-complete Riesz MV-algebras and $L$-measure spaces.}
\itemso{Greco, Salvatore (ed.) et al., Advances in computational intelligence. 14th international conference on information processing and management of uncertainty in knowledge-based systems, IPMU 2012, Catania, Italy, July 9--13, 2012. Proceedings, Part II. Berlin: Springer (ISBN 978-3-642-31714-9/pbk; 978-3-642-31715-6/ebook). Communications in Computer and Information Science 298, 226-234 (2012).}
\itemab
Summary: State-complete Riesz MV-algebras are a particular class of probability MV-algebras. We associate to any state-complete Riesz MV-algebra $(A,s)$ a measure space $(X,\Omega ,\mu)$ such that $(A,s)$ and $(L_1(\mu)_u,s_{\mu})$ are isometrically isomorphic Riesz MV-algebras, where $L_1(\mu)_u$ is an interval of $L_1(\mu)$ and $s_\mu$ is the integral. This result can be seen as an analogue of Kakutani's concrete representation for $L$-spaces and it leads to a categorical duality between Riesz MV-algebras and a special class of measure spaces (called $L$-measure spaces).
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\itemli{doi:10.1007/978-3-642-31715-6\_25}
\end