A probability measure on S^n is exchangeable if it is invariant under any of the n! permutations of coordinates.  We give a proof of a representation result for arbitrary measurable space S that such a measure is a mixture of product measures but the mixing measure may be signed (in sharp contest to de Finetti's theorem).  We then give a necessary and sufficient condition for extensibility to S^N where N>n, possibly infinity. We also mention some possible applications. This is joint work with Linglong Yuan.