  We show that there exists a strong uniform embedding from any proper metric
space into any Banach space without cotype. Then we prove a result concerning
the Lipschitz embedding of locally finite subsets of $\mathcal{L}_{p}$-spaces.
We use this locally finite result to construct a coarse bi-Lipschitz embedding
for proper subsets of any $\mathcal{L}_p$-space into any Banach space $X$
containing the $\ell_p^n$'s. Finally using an argument of G. Schechtman we
prove that for general proper metric spaces and for Banach spaces without
cotype a converse statement holds.
