  It is well known that every derivation of a von Neumann algebra into itself
is an inner derivation and that every derivation of a von Neumann algebra into
its predual is inner. It is less well known that every triple derivation
(defined below) of a von Neumann algebra into itself is an inner triple
derivation.We examine to what extent all triple derivations of a von Neumann
algebra into its predual are inner. This rarely happens but it comes close. We
prove a (triple) cohomological characterization of finite factors and a
zero-one law for factors. Namely, we show that for any factor, the linear space
of triple derivations into the predual, modulo the norm closure of the inner
triple derivations, has dimension 0 or 1: It is zero if and only if the factor
is finite.
