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On some functional equations from additive and non-additive measures-I

Published online by Cambridge University Press:  20 January 2009

PL Kannappan
PL Kannappan
Affiliation:
University of WaterlooWaterloo, Ontario
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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 equation

which 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 representation

which with the property of additivity yields the functional equation (1.1), (9, 10).

Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 23 , Issue 2 , June 1980 , pp. 145 - 150
Copyright
Copyright © Edinburgh Mathematical Society 1980

References

REFERENCES

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