  Suppose that $E$ is a uniformly complete vector lattice and $p_1,..., p_n$
are positive reals. We prove that the diagonal of the Fremlin projective tensor
product of $E_{(p_1)},..., E_{(p_n)}$ can be identified with $E_{(p)}$ where $p
= p_1+...+p_n$ and $E_{(p)}$ stands for the $p$-concavification of $E$. We also
provide a variant of this result for Banach lattices. This extends the main
result of [BBPTT].
