Inspired by the harmonic-analytic research of Harald Cramér and Arne Beurling, Esseen examined the accuracy of the approximation to the normal distribution in the central limit theorem in the case of independent and identically distributed summands.
Esseen's bound is now called "the Berry-Esseen theorem", because it was independently proved by Andrew C. Berry, also.
[2] In 1944 Esseen received his doctorate with a thesis on the Fourier analysis of probability distributions.
In 1949 he was appointed full professor of applied mathematics at the Royal Institute of Technology in Stockholm.
Some industrial applications were considered in his writings, for example, his studies on control theory and in telecommunications.