Next:Unified Mutual InformationUp:Properties of Unified Conditional

## Multivariate Cases

In this subsection, we shall extend the results studied in Section 6.2.1 for three or more random variables. These are given by the following properties:

Property 6.8. We have

orand

Property 6.9. We have

Property 6.10. We have
(i)
(ii)  for =2 and 3;
The equality sign holds in (i) and (ii) iff  and  are independent given Z, i.e., iff  or i,j,k.

Property 6.11. We have

Property 6.12. For all , we have

(i)
(ii)
(iii)
(iv)
Property 6.13. If
then for all , we have
(i)
(ii)
(iii)
Note 6.3. It is interesting to verify the properties 6.11, 6.12 and 6.13 for the measures ( and ) and to find the conditions of their validites.

21-06-2001
Inder Jeet Taneja
Departamento de Matemática - UFSC
88.040-900 Florianópolis, SC - Brazil