Khinchin's theorem on the factorization of distributions

Khinchin's theorem on the factorization of distributions says that every probability distribution P admits (in the convolution semi-group of probability distributions) a factorization P = P 1 ⊗ P 2 {\displaystyle P=P_{1}\otimes P_{2}} where P1 is a probability distribution without any indecomposable factor and P2 is a distribution that is either degenerate or is representable as the convolution of a finite or countable set of indecomposable distributions. The factorization is not unique, in general.

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