| Title:
|
Entropy-like functionals: conceptual background and some results (English) |
| Author:
|
Katětov, Miroslav |
| Language:
|
English |
| Journal:
|
Commentationes Mathematicae Universitatis Carolinae |
| ISSN:
|
0010-2628 (print) |
| ISSN:
|
1213-7243 (online) |
| Volume:
|
33 |
| Issue:
|
4 |
| Year:
|
1992 |
| Pages:
|
645-660 |
| . |
| Category:
|
math |
| . |
| Summary:
|
We describe a conceptual approach which provides a unified view of various entropy-like functionals on the class of semimetric spaces, endowed with a bounded measure. The entropy $E$ considered in the author's previous articles is modified so as to assume finite values for a fairly wide class of spaces which fail to be totally bounded. (English) |
| Keyword:
|
entropy-like functionals |
| Keyword:
|
Hartley value of a piece of information |
| Keyword:
|
moderate $E$-entropy |
| MSC:
|
94A17 |
| idZBL:
|
Zbl 0777.94006 |
| idMR:
|
MR1240186 |
| . |
| Date available:
|
2009-01-08T17:59:25Z |
| Last updated:
|
2012-04-30 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/118536 |
| . |
| Reference:
|
[H28] Hartley S.V.L.: Transmission of information.Bell System Tech. J. 7 , no. 3 (1978), 535-563. |
| Reference:
|
[K80a] Katětov M.: Extensions of the Shannon entropy to semimetrized measure spaces.Comment. Math. Univ. Carolinae 21 (1980), 171-192. MR 0566249 |
| Reference:
|
[K80b] Katětov M.: Correction to ``Extensions of the Shannon entropy to semimetrized measure spaces''.Comment. Math. Univ. Carolinae 21 (1980), 825-830. Zbl 0476.94014, MR 0597770 |
| Reference:
|
[K83] Katětov M.: Extended Shannon entropies I.Czechoslovak Math. J. 33 (108) (1983), 546-601. MR 0721088 |
| Reference:
|
[K85] Katětov M.: Extended Shannon entropies II.Czechoslovak Math. J. 35 (110) (1985), 565-616. MR 0809043 |
| Reference:
|
[K86a] Katětov M.: On extended Shannon entropies and the epsilon entropy.Comment. Math. Univ. Carolinae 27 (1986), 519-534. MR 0873625 |
| Reference:
|
[K86b] Katětov M.: On the Rényi dimension.Comment. Math. Univ. Carolinae 27 (1986), 741-753. MR 0874669 |
| Reference:
|
[K87] Katětov M.: On dimensions of semimetrized measure spaces.Comment. Math. Univ. Carolinae 28 (1987), 399-411. MR 0912568 |
| Reference:
|
[K88] Katětov M.: On the differential and residual entropy.Comment. Math. Univ. Carolinae 29 (1988), 319-349. MR 0957402 |
| Reference:
|
[K90] Katětov M.: On entropy-like functionals and codes for metrized probability spaces I.Comment. Math. Univ. Carolinae 31 (1990), 49-66. MR 1056171 |
| Reference:
|
[K92] Katětov M.: On entropy-like functionals and codes for metrized probability spaces II.Comment. Math. Univ. Carolinae 33 (1992), 79-95. MR 1173750 |
| Reference:
|
[KT59] Kolgomorov A., Tihomirov V.: $\varepsilon $-entropy and $\varepsilon $-capacity of sets in function spaces (in Russian).Uspehi Mat. Nauk 14 , no. 2 (1959), 3-86. MR 0112032 |
| Reference:
|
[PRR67] Posner E.C., Rodemich H., Rumsey H., Jr.: Epsilon entropy of stochastic processes.Ann. Math. Statist. 38 (1967), 1000-1020. Zbl 0168.18003, MR 0211457 |
| Reference:
|
[R59] Rényi A.: On the dimension and entropy of probability distributions.Acta Math. Acad. Sci. Hungar. 10 (1959), 193-215. MR 0107575 |
| Reference:
|
[S48] Shannon C.E.: A mathematical theory of communication.Bell System Tech. J. 27 (1948), 375-423, 623-656. Zbl 1154.94303, MR 0026286 |
| . |
