# On entropy-like functionals and codes for metrized probability spaces II

Commentationes Mathematicae Universitatis Carolinae (1992)

- Volume: 33, Issue: 1, page 79-95
- ISSN: 0010-2628

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topKatětov, Miroslav. "On entropy-like functionals and codes for metrized probability spaces II." Commentationes Mathematicae Universitatis Carolinae 33.1 (1992): 79-95. <http://eudml.org/doc/247394>.

@article{Katětov1992,

abstract = {In Part I, we have proved characterization theorems for entropy-like functionals $\delta $, $\lambda $, $E$, $\Delta $ and $\Lambda $ restricted to the class consisting of all finite spaces $P\in \mathfrak \{W\}$, the class of all semimetric spaces equipped with a bounded measure. These theorems are now extended to the case of $\delta $, $\lambda $ and $E$ defined on the whole of $\mathfrak \{W\}$, and of $\Delta $ and $\Lambda $ restricted to a certain fairly wide subclass of $\mathfrak \{W\}$.},

author = {Katětov, Miroslav},

journal = {Commentationes Mathematicae Universitatis Carolinae},

keywords = {regular code; dyadic expansion; entropy; regular code; dyadic expansion; entropy-like functionals},

language = {eng},

number = {1},

pages = {79-95},

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

title = {On entropy-like functionals and codes for metrized probability spaces II},

url = {http://eudml.org/doc/247394},

volume = {33},

year = {1992},

}

TY - JOUR

AU - Katětov, Miroslav

TI - On entropy-like functionals and codes for metrized probability spaces II

JO - Commentationes Mathematicae Universitatis Carolinae

PY - 1992

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

VL - 33

IS - 1

SP - 79

EP - 95

AB - In Part I, we have proved characterization theorems for entropy-like functionals $\delta $, $\lambda $, $E$, $\Delta $ and $\Lambda $ restricted to the class consisting of all finite spaces $P\in \mathfrak {W}$, the class of all semimetric spaces equipped with a bounded measure. These theorems are now extended to the case of $\delta $, $\lambda $ and $E$ defined on the whole of $\mathfrak {W}$, and of $\Delta $ and $\Lambda $ restricted to a certain fairly wide subclass of $\mathfrak {W}$.

LA - eng

KW - regular code; dyadic expansion; entropy; regular code; dyadic expansion; entropy-like functionals

UR - http://eudml.org/doc/247394

ER -

## References

top- 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., Extended Shannon entropies, Czechoslovak Math. J. 33 (108) (1983), 546-601. (1983) MR0721088
- Kolgomorov A., On some asymptotic characteristics of totally bounded spaces (in Russian), Doklady Akad. Nauk SSSR 108 (1956), 385-389. (1956)
- 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

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