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.