Cramér–Wold theorem
In mathematics, the Cramér–Wold theorem in measure theory states that a Borel probability measure on is uniquely determined by the totality of its one-dimensional projections. It is used as a method for proving joint convergence results. The theorem is named after Harald Cramér and Herman Ole Andreas Wold.
Let
and
be random vectors of dimension k. Then converges in distribution to if and only if:
for each, that is, if every fixed linear combination of the coordinates of converges in distribution to the correspondent linear combination of coordinates of.Footnotes
