No measurable solutions exist for f(x) + g(y) = h(x,y) when h is Borel measurable and associated with uniform or Cauchy distribution characterizations, proved via Dirac measure properties.
Arnold, Some characterizations of the Cauchy distribution , Australian Journal of Statistics 21 (1979), 166–169
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Non-existence of measurable solutions of certain functional equations via probabilistic approaches
No measurable solutions exist for f(x) + g(y) = h(x,y) when h is Borel measurable and associated with uniform or Cauchy distribution characterizations, proved via Dirac measure properties.