# Entropy-like functionals: conceptual background and some results

Commentationes Mathematicae Universitatis Carolinae (1992)

- Volume: 33, Issue: 4, page 645-660
- ISSN: 0010-2628

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topKatětov, Miroslav. "Entropy-like functionals: conceptual background and some results." Commentationes Mathematicae Universitatis Carolinae 33.4 (1992): 645-660. <http://eudml.org/doc/247355>.

@article{Katětov1992,

abstract = {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.},

author = {Katětov, Miroslav},

journal = {Commentationes Mathematicae Universitatis Carolinae},

keywords = {entropy-like functionals; Hartley value of a piece of information; moderate $E$-entropy; Hartley value of a piece of information; moderate -entropy; entropy- like functionals},

language = {eng},

number = {4},

pages = {645-660},

publisher = {Charles University in Prague, Faculty of Mathematics and Physics},

title = {Entropy-like functionals: conceptual background and some results},

url = {http://eudml.org/doc/247355},

volume = {33},

year = {1992},

}

TY - JOUR

AU - Katětov, Miroslav

TI - Entropy-like functionals: conceptual background and some results

JO - Commentationes Mathematicae Universitatis Carolinae

PY - 1992

PB - Charles University in Prague, Faculty of Mathematics and Physics

VL - 33

IS - 4

SP - 645

EP - 660

AB - 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.

LA - eng

KW - entropy-like functionals; Hartley value of a piece of information; moderate $E$-entropy; Hartley value of a piece of information; moderate -entropy; entropy- like functionals

UR - http://eudml.org/doc/247355

ER -

## References

top- Hartley S.V.L., Transmission of information, Bell System Tech. J. 7 , no. 3 (1978), 535-563. (1978)
- Katětov M., Extensions of the Shannon entropy to semimetrized measure spaces, Comment. Math. Univ. Carolinae 21 (1980), 171-192. (1980) MR0566249
- Katětov M., Correction to ``Extensions of the Shannon entropy to semimetrized measure spaces'', Comment. Math. Univ. Carolinae 21 (1980), 825-830. (1980) Zbl0476.94014MR0597770
- Katětov M., Extended Shannon entropies I, Czechoslovak Math. J. 33 (108) (1983), 546-601. (1983) MR0721088
- Katětov M., Extended Shannon entropies II, Czechoslovak Math. J. 35 (110) (1985), 565-616. (1985) MR0809043
- Katětov M., On extended Shannon entropies and the epsilon entropy, Comment. Math. Univ. Carolinae 27 (1986), 519-534. (1986) MR0873625
- Katětov M., On the Rényi dimension, Comment. Math. Univ. Carolinae 27 (1986), 741-753. (1986) MR0874669
- Katětov M., On dimensions of semimetrized measure spaces, Comment. Math. Univ. Carolinae 28 (1987), 399-411. (1987) MR0912568
- Katětov M., On the differential and residual entropy, Comment. Math. Univ. Carolinae 29 (1988), 319-349. (1988) MR0957402
- Katětov M., On entropy-like functionals and codes for metrized probability spaces I, Comment. Math. Univ. Carolinae 31 (1990), 49-66. (1990) MR1056171
- Katětov M., On entropy-like functionals and codes for metrized probability spaces II, Comment. Math. Univ. Carolinae 33 (1992), 79-95. (1992) MR1173750
- Kolgomorov A., Tihomirov V., $\epsilon $-entropy and $\epsilon $-capacity of sets in function spaces (in Russian), Uspehi Mat. Nauk 14 , no. 2 (1959), 3-86. (1959) MR0112032
- Posner E.C., Rodemich H., Rumsey H., Jr., Epsilon entropy of stochastic processes, Ann. Math. Statist. 38 (1967), 1000-1020. (1967) Zbl0168.18003MR0211457
- Rényi A., On the dimension and entropy of probability distributions, Acta Math. Acad. Sci. Hungar. 10 (1959), 193-215. (1959) MR0107575
- Shannon C.E., A mathematical theory of communication, Bell System Tech. J. 27 (1948), 375-423, 623-656. (1948) Zbl1154.94303MR0026286

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