Abstract
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.
Similar content being viewed by others
References
D. Butnariu and E. P. Klement: Triangular norm-based measures and their Markov kernel representation. J. Math. Anal. Appl. 169 (1991), 111–143.
A. Dvurečenskij and S. Pulmannová: Difference posets, effects and quantum measurements. Internat. J. Theoret. Phys. 33 (1994), 819–850.
F. Chovanec and F. Kôpka: On a representation of observables in D-posets of fuzzy sets. Tatra Mt. Math. Publ. 1 (1992), 19–24.
M. Jurečková and B. Riečan: On the strong law of large numbers in D-posets. Internat. J. Theoret. Phys 34 (1995), 1495–1500.
F. Kôpka and F. Chovanec: D-posets. Math. Slovaca 44 (1994), 21–34.
R. Mesiar: Fuzzy observables. J. Math. Anal. Appl. 174 (1993), 178–193.
R. Mesiar and B. Riečan: On the joint observables in some quantum structures. Tatra Mt. Math. Publ. 3 (1993), 183–190.
B. Riečan: Upper and lower limits of sequences of observables in D-posets of fuzzy sets. Math. Slovaca 46 (1996), 419–431.
P. Walters: Ergodic Theory—Introductory Lectures. Springer, Berlin, 1975.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Riečan, B. On The Individual Ergodic Theorem In D-Posets of Fuzzy Sets. Czechoslovak Mathematical Journal 50, 673–680 (2000). https://doi.org/10.1023/A:1022439925578
Issue Date:
DOI: https://doi.org/10.1023/A:1022439925578