  It is shown that white noise is an invariant measure for the Korteweg-deVries
equation on $\mathbb T$. This is a consequence of recent results of Kappeler
and Topalov establishing the well-posedness of the equation on appropriate
negative Sobolev spaces, together with a result of
  Cambronero and McKean that white noise is the image under the Miura transform
(Ricatti map) of the (weighted) Gibbs measure for the modified KdV equation,
proven to be invariant for that equation by Bourgain.
