In mathematics, the Cramér–Wold theorem[1][2] or the Cramér–Wold device[3][4] is a theorem in measure theory and which states that a Borel probability measure on
is uniquely determined by the totality of its one-dimensional projections.
[5][6][7] It is used as a method for proving joint convergence results.
The theorem is named after Harald Cramér and Herman Ole Andreas Wold, who published the result in 1936.
[8] Let and be random vectors of dimension k. Then
converges in distribution to
, that is, if every fixed linear combination of the coordinates of
converges in distribution to the correspondent linear combination of coordinates of
[10] This mathematical analysis–related article is a stub.