Extension of domains of states |
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| Authors: | Roman Frič |
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| Affiliation: | (1) Mathematical Institute, Slovak Academy of Sciences, Grešákova 6, 040 01 Košice, Slovak Republic;(2) Catholic University in Ružomberok, Nám. A. Hlinku 56/1, 034 01 Ružomberok, Slovak Republic |
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| Abstract: | We deal with categorical aspects of the extensions of generalized probability measures. In particular, we study various domains
of fuzzy sets, describe the relationships between σ-fields of crisp sets and generated Łukasiewicz tribes of measurable functions, and mention some probabilistic aspects. D-posets and sequential continuity play an important role.
This work was supported by the Slovak Research and Development Agency under the contract No. APVV-0071-06, Protocol for Scientific
and Technological Collaboration between the Republic of Italy and Slovak Republic, Project No. 15: Algebraic and Logical Systems
of Soft Computing, and VEGA 2/6088/26. |
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| Keywords: | Lukasiewicz tribe Field of sets MV-algebra D-poset od fuzzy sets Sequentially continuous D-homomorphism Probability measure State Extension of states Epireflection Measurable space Duality Fuzzy random variable Observable |
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