Cramér’s decomposition theorem for a normal distribution is a result of probability theory.
The latter result, initially announced by Paul Lévy,[1] has been proved by Harald Cramér.
[2] This became a starting point for a new subfield in probability theory, decomposition theory for random variables as sums of independent variables (also known as arithmetic of probabilistic distributions).
[3] Let a random variable ξ be normally distributed and admit a decomposition as a sum ξ=ξ1+ξ2 of two independent random variables.
A proof of Cramér's decomposition theorem uses the theory of entire functions.