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 . If takes values in , then the statement is also true with . Footnotes References External links Project Euclid: "When is a probability measure determined by infinitely many projections?" Theorems in measure theory Probability theorems Convergence (mathematics)