a function with poles off $K$ $\langle$vanishing off $K\rangle$
an extension of $f$ off $U$
The kernel is $C^0$ on $X\times X$ off the diagonal.
a Blaschke product with at least one zero off the origin
If we stay a fixed distance off the critical line, we do not expect Benford behaviour.
We close this off by characterizing ......
Let $M'$ be the minor obtained by crossing off the last row and column of $M$.
Continuity then finishes off the argument.
This can be read off from (8).