Resumen
Let Z=(Z^(^1^),Z^(^2^)) be an s-variate random vector partitioned into r- and q-variate subvectors whose distribution depends on an s-variate location parameter @q=(@q^(^1^),@q^(^2^)) partitioned in the same way as Z. For the sxs matrix I of Fisher information on @q contained in Z and rxr and qxq matrices I"1 and I"2 of Fisher information on @q^(^1^) and @q^(^2^) in Z^(^1^) and Z^(^2^), it is proved that trace(I^-^1)==trace(I@^^(^1^))+trace(I@^^(^2^)).