Liouville is off the grid

Show that any function f:\mathbb{Z}\times\mathbb{Z}\to (0,1) that verifies

f(m,n)=\dfrac{f(m-1,n)+f(m+1,n) + f(m,n-1)+f(m,n+1)}{4}

must be constant.

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Liouville is off the grid

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