How many projections suffice to determine a probability  measure ?
A sharp form of the Cramér-Wold theorem


Juan Antonio Cuesta-Albertos, Ricardo Fraiman and Thomas Ransford


Universidad de Cantabria, Spain


The Cramér-Wold theorem states that a Borel probability measure $P$ on $R^d$ is uniquely determined by its one-dimensional projections. We prove a sharp form of this result, addressing the problem of how large a subset of these projections is really needed to determine $P$. We also consider extensions of our results to  measures on a separable Hilbert space.