caa a22 4500 465825001 CHVBK 20180323112146.0 cr unu---uuuuu 170327e19900201xx s 000 0 eng 10.1007/BF01833946 doi (NATIONALLICENCE)springer-10.1007/BF01833946 Ebanks B. Department of Mathematics, University of Louisville, 40292, Louisville, Kentucky, USA aut Branching inset entropies on open domains [Elektronische Daten] [B. Ebanks] Summary: The forms of all semisymmetric, branching, multidimensional measures of inset information on open domains are determined. This is done for both the complete and the possibly incomplete partition cases. The key to these results is to find the general solution of the functional equation $$(*)\Delta \left( {\begin{array}{*{20}c} {E,F} \\ {p,q} \\ \end{array} } \right) + \Delta \left( {\begin{array}{*{20}c} {E \cup F,G} \\ {p + q,r} \\ \end{array} } \right) = \Delta \left( {\begin{array}{*{20}c} {E,G} \\ {p,r} \\ \end{array} } \right) + \Delta \left( {\begin{array}{*{20}c} {E \cup G,F} \\ {p + r,q} \\ \end{array} } \right)$$ for all(p, q, r) ∈ D 3 :={(p 1 , p 2 , p 3 )∣p i ∈]0, 1[ k (i = 1,2,3),p 1 + p 2 + p 3 ∈]0, 1[ k } and all (E, F, G) for which there exists anH with (E, F, G, H) ∈ ℒ4:={(E 1 ,⋯,E 4 )∣ E i ∈ ℛ\{Ø},E 1∩E j = Ø for alli ≠ j}. Here, ℛ is a ring of subsets of a given universal set. Functional equation (*) is solved by use of the general solution of the generalized characteristic equation of branching information measures. Birkhäuser Verlag, 1990 Primary 94A17, 39B50 nationallicence Secondary 39B40, 39B70 nationallicence aequationes mathematicae Birkhäuser-Verlag 39/1(1990-02-01), 100-113 0001-9054 39:1<100 1990 39 10 https://doi.org/10.1007/BF01833946 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/BF01833946 text/html Onlinezugriff via DOI NATIONALLICENCE 100 1- Ebanks B. Department of Mathematics, University of Louisville, 40292, Louisville, Kentucky, USA aut NATIONALLICENCE 773 0- aequationes mathematicae Birkhäuser-Verlag 39/1(1990-02-01), 100-113 0001-9054 39:1<100 1990 39 10 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer