# zbMATH — the first resource for mathematics

The dynamics of $$F$$-quantum spaces. (English) Zbl 1016.60002
The paper is devoted to the study of the concept of isomorphisms and conjugation of $$F$$-quantum dynamical systems. It is proved that isomorphism implies conjugacy in the dynamics of $$F$$-quantum spaces.

##### MSC:
 60A10 Probabilistic measure theory
Full Text:
##### References:
 [1] BROWN J. R.: Ergodic Theory and Topological Dynamics. Academic Press Inc., London, 1976. · Zbl 0334.28011 [2] BUTNARIU D.: Additive fuzzy measures and integrals. J. Math. Anal. Appl. 93 (1983), 436-452. · Zbl 0516.28006 [3] DUMITRESCU D.: Fuzzy measures and the entropy of fuzzy partitions. J. Math. Anal. Appl. 176 (1993), 359-373. · Zbl 0782.28012 [4] KLEMENT E. P.: Fuzzy $$\sigma$$-algebras and fuzzy measurable functions. Fuzzy Sets and Systems 4 (1980), 83-93. · Zbl 0444.28001 [5] MARKECHOVÁ D.: The entropy of an $$F$$-quantum space. Math. Slovaca 40 (1990), 177-190. · Zbl 0735.28011 [6] MARKECHOVÁ D.: The conjugation of fuzzy probability space to the unit interval. Fuzzy Sets and Systems 47 (1992), 87-92. · Zbl 0754.60004 [7] MARKECHOVÁ D.: $$F$$-quantum spaces and their dynamics. Fuzzy Sets and Systems 50 (1992), 79-88. · Zbl 0791.03037 [8] KHARE M.: Fuzzy a-algebras and conditional entropy. Fuzzy Sets and Systems 102 (1999), 287-292. · Zbl 0935.28011 [9] KHARE M.: /: Metric entropy and sufficient families. Indian J. Math. 41 (1999), 191-204. · Zbl 1032.28010 [10] KHARE M.: Sufficient families and entropy of inverse limit. Math. Slovaca 49 (1999), 443-452. · Zbl 0956.37005 [11] PIASECKI K.: Probability of fuzzy events defined as denumerable additivity measure. Fuzzy Sets and Systems 17 (1985), 271-284. · Zbl 0604.60005 [12] RIECAN B.: A new approach to some notions of statistical quantum mechanics. Busefal 35 (1988), 4-6. [13] RIEČAN B.-DVURENČENSKIJ A.: On randomness and fuzziness. Progress in Fuzzy Sets in Europe, Warszaw, 1986. [14] SRIVASTAVA P.-KHARE M.: Conditional entropy and Rokhlin metric. Math. Slovaca 49 (1999), 433-441. · Zbl 0949.28015 [15] SRIVASTAVA P.-KHARE M.-SRIVASTAVA Y. K.: A fuzzy measure algebra as a metric space. Fuzzy Sets and Systems 79 (1996), 395-400. · Zbl 0872.28012 [16] SRIVASTAVA P.-KHARE M.-SRIVASTAVA Y. K.: m-equivalence, entropy and $$F$$-dynamical systems. Fuzzy Sets and Systems 121 (2001), 275-283. · Zbl 0982.37006
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.