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We present a general method for the extension of results about linear prediction for q-variate weakly stationary processes on a separable locally compact abelian group $G_2$ (whose dual is a Polish space) with known values of the processes on a separable subset $S_2\subseteq G_2$ to results for weakly stationary processes on $G_1\times G_2$ with observed values on $G_1\times S_2$. In particular, the method is applied to obtain new proofs of some well-known results of Ze Pei Jiang.