A Sharp Form of the Cramér–wold Theorem
نویسندگان
چکیده
The Cramér–Wold theorem states that a Borel probability measure P on R 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. As an application of these ideas, we derive a simple, universally consistent goodness-of fit-test for data taking values in a Hilbert space.
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