
316 7
Restoration
As for the case of topmost row points, (169) implies that points on the leftmost
column should obey (164c).
Coming to the proof of the theorem, let us assume that the field is wide-
sense Markov; we then want to show that (166) is true. Note that from (160)
[(168) and (169) for points on the top and left boundary] each %{m
y
ri) is
orthogonal to
f(p,q)
for all
(p,q)eX
mn
.
Now ξ(/:,/) for any (kj) e X
mn
is a linear combination of f (/?, ^)'s in
X
mt
„.
Therefore, ξ(λ??, η) must be orthog-
onal to ξ(&,/) for all
(k,l)eX
mn
.
Since this must be true for every (m,n)
in the picture, it follows that
E{$(p,q)$(m,n)} = 0, ρ φ m or qφn
whic ...