2.2. Products. Given median spaces X1; X2, we can consider the product X1 X2, which is a median space itself with the `1 metric, i.e.
where the first two pieces are transverse and the third is null. Since h 2 H0 and k 2 H n (H0 [ H ) this partition is nontrivial. Finally, observe that H0 is inseparable and, thus, measurable. Corollary 2.9 now violates the irreducibility of X.
with ah ( h0 and bk ( k0; in particular, h; ah ; k; bk form a facing 4-tuple.
Set w := fh; h g 2 W and := h \ ah \ k \ bk X. Claim. For every nontrivial, reduced word u in a and b, if u = au0, we have u ah ; if u = a 1u0, we have u h; if u = bu0, we have u bk ; if u = b 1u0, we have u k.
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