On some functional equations from additive and non-additive measures-I
1980 ◽
Vol 23
(2)
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pp. 145-150
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Keyword(s):
It is known that while the Shannon and the Rényi entropies are additive, the measure entropy of degree β proposed by Havrda and Charvat (7) is non-additive. Ever since Chaundy and McLeod (4) considered the following functional equationwhich arose in statistical thermodynamics, (1.1) has been extensively studied (1, 5, 6, 8). From the algebraic properties of symmetry, expansibility and branching of the entropy (viz. Shannon entropy Hn, etc.) one obtains the sum representationwhich with the property of additivity yields the functional equation (1.1), (9, 10).
1969 ◽
Vol 12
(6)
◽
pp. 837-846
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1988 ◽
Vol 38
(3)
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pp. 351-356
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Keyword(s):
1985 ◽
Vol 97
(2)
◽
pp. 261-278
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1960 ◽
Vol 3
(2)
◽
pp. 113-120
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2016 ◽
Vol 94
(2)
◽
pp. 278-285
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Keyword(s):
2012 ◽
Vol 85
(2)
◽
pp. 202-216
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Keyword(s):
1970 ◽
Vol 11
(3)
◽
pp. 362-366
◽
Keyword(s):
2012 ◽
Vol 85
(2)
◽
pp. 191-201
◽
Keyword(s):
2013 ◽
Vol 89
(1)
◽
pp. 33-40
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