On Some Functional Equations from Additive and Nonadditive Measures - II
Copyright policy )On Some Functional Equations from Additive and Nonadditive Measures - II
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).
- University of Waterloo Canada
additivity, additive properties, Measures of information, entropy, measures of information, `sum form' functional equations, general Lebesgue measurable solution, additive and non-additive measures, measure entropy, entropy of degree beta, weighted entropy, measure of information, directed divergence, sum functional equations, sum representation, Shannon entropy, additive measures, measurable solution, Shannon-Renyi entropies, Functional inequalities, including subadditivity, convexity, etc., Shannon's entropy, measurable solutions, additive and nonadditive measures, Functional equations and inequalities
additivity, additive properties, Measures of information, entropy, measures of information, `sum form' functional equations, general Lebesgue measurable solution, additive and non-additive measures, measure entropy, entropy of degree beta, weighted entropy, measure of information, directed divergence, sum functional equations, sum representation, Shannon entropy, additive measures, measurable solution, Shannon-Renyi entropies, Functional inequalities, including subadditivity, convexity, etc., Shannon's entropy, measurable solutions, additive and nonadditive measures, Functional equations and inequalities
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