  Let V be a quadratic space with a form q over an arbitrary local field F of
characteristic different from 2. Let $W=V \oplus Fe$ with the form Q extending
q with Q(e)=1. Consider the standard embedding of O(V) into O(W) and the
two-sided action of $O(V)\times O(V)$ on $O(W)$.
  In this note we show that any $O(V)\times O(V)$-invariant distribution on
O(W) is invariant with respect to transposition. This result was earlier proven
in a bit different form in [vD] for F=R, in [AvD] for F=C and in [BvD] for
p-adic fields. Here we give a different proof.
  Using results from [AGS], we show that this result on invariant distributions
implies that the pair (O(V),O(W)) is a Gelfand pair. In the archimedean setting
this means that for any irreducible admissible smooth Frechet representation E
of O(W) we have $dim Hom_{O(V)}(E,C) \leq 1.$
  A stronger result for p-adic fields is obtained in [AGRS].
