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Article

Keywords:
individual ergodic theorem; $d$-posets of fuzzy sets; state and observable
Summary:
Calculus for observables in a space of functions from an abstract set to the unit interval is developed and then the individual ergodic theorem is proved.
References:
[1] D. Butnariu and E. P. Klement: Triangular norm-based measures and their Markov kernel representation. J. Math. Anal. Appl. 169 (1991), 111–143. DOI 10.1016/0022-247X(91)90181-X | MR 1135265
[2] A. Dvurečenskij and S. Pulmannová: Difference posets, effects and quantum measurements. Internat. J. Theoret. Phys. 33 (1994), 819–850. DOI 10.1007/BF00672820 | MR 1286161
[3] F. Chovanec and F. Kôpka: On a representation of observables in $D$-posets of fuzzy sets. Tatra Mt. Math. Publ. 1 (1992), 19–24. MR 1230458
[4] M. Jurečková and B. Riečan: On the strong law of large numbers in $D$-posets. Internat. J. Theoret. Phys 34 (1995), 1495–1500. DOI 10.1007/BF00676259 | MR 1353692
[5] F. Kôpka and F. Chovanec: $D$-posets. Math. Slovaca 44 (1994), 21–34. MR 1290269
[6] R. Mesiar: Fuzzy observables. J. Math. Anal. Appl. 174 (1993), 178–193. DOI 10.1006/jmaa.1993.1109 | MR 1212925 | Zbl 0777.60005
[7] R. Mesiar and B. Riečan: On the joint observables in some quantum structures. Tatra Mt. Math. Publ. 3 (1993), 183–190. MR 1278533
[8] B. Riečan: Upper and lower limits of sequences of observables in $D$-posets of fuzzy sets. Math. Slovaca 46 (1996), 419–431. MR 1472636
[9] P. Walters: Ergodic Theory—Introductory Lectures. Springer, Berlin, 1975. MR 0480949 | Zbl 0299.28012
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