Cramér–Wold theorem

The set of Cramér -Wold ( by Harald Cramér and Herman Wold ) from measure theory says that a Borel measure on is uniquely determined by all its one-dimensional projections. This explains why it is sufficient in statistical methods such as the Grand Tour or Projection Pursuit to look at projections of the data. It was published in 1936.

Let and two -dimensional random variables. Then we have

Each (fixed ) linear combination of converges in distribution to the corresponding linear combination of exactly when to converge in distribution. This means the convergence in distribution of a multivariate random variable can ( just the linear combinations ) can be attributed to the convergence in distribution of a univariate random variables.