  In [AGRS] a multiplicity one theorem is proven for general linear groups,
orthogonal groups and unitary groups ($GL, O,$ and $U$) over $p$-adic local
fields. That is to say that when we have a pair of such groups $G_n\subseteq
G_{n+1}$, any restriction of an irreducible smooth representation of $G_{n+1}$
to $G_n$ is multiplicity free. This property is already known for $GL$ over a
local field of positive characteristic, and in this paper we also give a proof
for $O,U$, and $SO$ over local fields of positive odd characteristic. These
theorems are shown in [GGP] to imply the uniqueness of Bessel models, and in
[CS] to imply the uniqueness of Rankin-Selberg models. We also prove
simultaniously the uniqeuness of Fourier-Jacobi models, following the outlines
of the proof in [Sun]. By the Gelfand-Kazhdan criterion, the multiplicity one
property for a pair $H\leq G$ follows from the statement that any distribution
on $G$ invariant to conjugations by $H$ is also invariant to some
anti-involution of $G$ preserving $H$.
