We can find a neighbourhood $W$ of the identity in $T$ and a number $\psi>0$ to the following effect. If $g,J,A$ is a set of data on $U$ with

• •

  $$\|g-g_{0}\|_{U}\leq\psi,\|J-J_{0}\|_{U}\leq\psi;$$

• •

  $g(A,A_{0})=1$;

• •

  $\tau(A,A_{0})\in W$;

then$(g,J,A)$ has Property (H).