Entropy-like functionals: conceptual background and some results

Miroslav Katětov

Commentationes Mathematicae Universitatis Carolinae (1992)

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

Abstract

top
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.

How to cite

top

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

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

                
Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.