| Title:
|
On the individual ergodic theorem in $D$-posets of fuzzy sets (English) |
| Author:
|
Riečan, Beloslav |
| Language:
|
English |
| Journal:
|
Czechoslovak Mathematical Journal |
| ISSN:
|
0011-4642 (print) |
| ISSN:
|
1572-9141 (online) |
| Volume:
|
50 |
| Issue:
|
4 |
| Year:
|
2000 |
| Pages:
|
673-680 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| 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. (English) |
| Keyword:
|
individual ergodic theorem |
| Keyword:
|
$d$-posets of fuzzy sets |
| Keyword:
|
state and observable |
| MSC:
|
28E10 |
| MSC:
|
37A30 |
| MSC:
|
58F11 |
| idZBL:
|
Zbl 1079.28504 |
| idMR:
|
MR1792963 |
| . |
| Date available:
|
2009-09-24T10:36:58Z |
| Last updated:
|
2020-07-03 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/127603 |
| . |
| Reference:
|
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| Reference:
|
[2] A. Dvurečenskij and S. Pulmannová: Difference posets, effects and quantum measurements.Internat. J. Theoret. Phys. 33 (1994), 819–850. MR 1286161, 10.1007/BF00672820 |
| Reference:
|
[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 |
| Reference:
|
[4] M. Jurečková and B. Riečan: On the strong law of large numbers in $D$-posets.Internat. J. Theoret. Phys 34 (1995), 1495–1500. MR 1353692, 10.1007/BF00676259 |
| Reference:
|
[5] F. Kôpka and F. Chovanec: $D$-posets.Math. Slovaca 44 (1994), 21–34. MR 1290269 |
| Reference:
|
[6] R. Mesiar: Fuzzy observables.J. Math. Anal. Appl. 174 (1993), 178–193. Zbl 0777.60005, MR 1212925, 10.1006/jmaa.1993.1109 |
| Reference:
|
[7] R. Mesiar and B. Riečan: On the joint observables in some quantum structures.Tatra Mt. Math. Publ. 3 (1993), 183–190. MR 1278533 |
| Reference:
|
[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 |
| Reference:
|
[9] P. Walters: Ergodic Theory—Introductory Lectures.Springer, Berlin, 1975. Zbl 0299.28012, MR 0480949 |
| . |
