On measurable solutions of a functional equation and their application to information theory

Gur Dial

Aplikace matematiky (1983)

  • Volume: 28, Issue: 2, page 103-107
  • ISSN: 0862-7940

Abstract

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In this paper, measurable solutions of a functional equation with four unknown functions are obtained. As an application of the measurable solutions a joint characterization of Shannon’s entropy and entropy of type β is given.

How to cite

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Dial, Gur. "On measurable solutions of a functional equation and their application to information theory." Aplikace matematiky 28.2 (1983): 103-107. <http://eudml.org/doc/15281>.

@article{Dial1983,
abstract = {In this paper, measurable solutions of a functional equation with four unknown functions are obtained. As an application of the measurable solutions a joint characterization of Shannon’s entropy and entropy of type $\beta $ is given.},
author = {Dial, Gur},
journal = {Aplikace matematiky},
keywords = {measurable solutions; system; Shannon’s entropy; measurable solutions; system; Shannon's entropy},
language = {eng},
number = {2},
pages = {103-107},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {On measurable solutions of a functional equation and their application to information theory},
url = {http://eudml.org/doc/15281},
volume = {28},
year = {1983},
}

TY - JOUR
AU - Dial, Gur
TI - On measurable solutions of a functional equation and their application to information theory
JO - Aplikace matematiky
PY - 1983
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 28
IS - 2
SP - 103
EP - 107
AB - In this paper, measurable solutions of a functional equation with four unknown functions are obtained. As an application of the measurable solutions a joint characterization of Shannon’s entropy and entropy of type $\beta $ is given.
LA - eng
KW - measurable solutions; system; Shannon’s entropy; measurable solutions; system; Shannon's entropy
UR - http://eudml.org/doc/15281
ER -

References

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  1. J. Aczel, Lectures on functional equations and their applications, Academic Press, New York, 1966. (1966) Zbl0139.09301MR0208210
  2. J. Aczel Z. Daroczy, On measures of information and their characterizations, Academic Press, New York, 1975. (1975) MR0689178
  3. Z. Daroczy, Losonczi, Über die Erweiterung der auf einer Punktmenge additive Funktion, Publ Math. Debrecen, 14 (1967) 239-245. (1967) MR0240492
  4. I. J. Taneja, A joint characterization of Shannons entropy of type through a functional equation, Journal of Mathematical Sciences, (10, 1975), 69-74. (1975) MR0539497

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