Weighted additive information measures

Wolfgang Sander

International Journal of Mathematics and Mathematical Sciences, 1990, vol. 13, 1-7

Abstract:

We determine all measurable functions I , G , L : [ 0 , 1 ] → ℝ satisfying the functional equation ∑ i = 1 n ∑ j = 1 m I ( p i , q j ) = ∑ i = 1 n ∑ j = 1 m G ( p i ) I ( q j ) + ∑ i = 1 n ∑ j = 1 m L ( q j ) I ( p i ) for P ∈ Γ n , Q ∈ Γ m and for a fixed pair ( n , m ) , n ≥ 3 , m ≥ 3 , where G ( 0 ) = L ( 0 ) = 0 and G ( 1 ) = L ( 1 ) = 1 . This functional equation has interesting applications in information theory.

Date: 1990
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jijmms:292796

DOI: 10.1155/S0161171290000631

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