On entropy-like functionals and codes for metrized probability spaces. I.

Miroslav Katětov

Commentationes Mathematicae Universitatis Carolinae (1990)

  • Volume: 031, Issue: 1, page 49-66
  • ISSN: 0010-2628

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Katětov, Miroslav. "On entropy-like functionals and codes for metrized probability spaces. I.." Commentationes Mathematicae Universitatis Carolinae 031.1 (1990): 49-66. <http://eudml.org/doc/17808>.

@article{Katětov1990,
author = {Katětov, Miroslav},
journal = {Commentationes Mathematicae Universitatis Carolinae},
keywords = {Hamming space; regular code; entropic content; pre-entropy; final entropy; entropy-like functionals; semimetric spaces; Shannon entropy; finite probability space},
language = {eng},
number = {1},
pages = {49-66},
publisher = {Charles University in Prague, Faculty of Mathematics and Physics},
title = {On entropy-like functionals and codes for metrized probability spaces. I.},
url = {http://eudml.org/doc/17808},
volume = {031},
year = {1990},
}

TY - JOUR
AU - Katětov, Miroslav
TI - On entropy-like functionals and codes for metrized probability spaces. I.
JO - Commentationes Mathematicae Universitatis Carolinae
PY - 1990
PB - Charles University in Prague, Faculty of Mathematics and Physics
VL - 031
IS - 1
SP - 49
EP - 66
LA - eng
KW - Hamming space; regular code; entropic content; pre-entropy; final entropy; entropy-like functionals; semimetric spaces; Shannon entropy; finite probability space
UR - http://eudml.org/doc/17808
ER -

References

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  1. J. Balatoni A. Rényi, On the notion of entropy, (Hungarian), Publ. Math. Inst. Hungarian Acad. Sci. 1 (1956), 9-40. English translation: Selected papers of A. Renyi, vol. I, pp. 558-584, Akademiai Kiado, Budapest, 1976. (1956) Zbl0074.33703
  2. M. Katětov, Extended Shannon entropies I, Czechoslovak Math. J. 33 (108) (1983), 564-601. (1983) Zbl0542.94007MR0721088
  3. M. Katětov, Extended Shannon entropies II, Czechoslovak Math. J. 35 (110) (1985), 565-616. (1985) Zbl0601.94004MR0809043
  4. M. Katětov, On the Rényi dimension, Comment. Math. Univ. Carolinae 27 (1986), 741-753. (1986) Zbl0605.94002MR0874669
  5. M. Katětov, On dimensions of semimetrixed measure spaces, Comment. Math. Univ. Carolinae 28 (1987), 399-411. (1987) Zbl0648.94003MR0912568
  6. M. Katětov, On the differential and residual entropy, Comment. Math. Univ. Carolinae 29 (1988), 319-349. (1988) Zbl0649.94006MR0957402
  7. A. Kolmogorov, On some asymptotic characteristics of totally bounded metric spaces, (Russian), Doklady Akad. Nauk SSSR 108 (1956), 385-389. (1956) Zbl0070.11501MR0080904
  8. A. Kolmogorov V. Tihomirov, ε -entropy and ε - capacity of sets in function spaces, (Russian), Uspehi Mat. Nauk 14, no. 2 (1959), 3-86. (1959) MR0112032
  9. A. Rényi, On the dimension and entropy of probability distributions, Acta Math. Acad. Sci. Hung. 10 (1959), 193-215. (1959) Zbl0088.10702MR0107575
  10. A. Rényi, Dimension, entropy and information, Trans. 2nd Prague Conf. Information Theory, pp. 545-556, Prague, 1960. (1960) Zbl0115.35502MR0129049

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