Summary
Letℱ denote the convolution semigroup of probability distributions on the real line. We prove thatno element of ℱ is prime in the sense that given anℱ one can always find two distributionsG,H∈ℱ such thatF is a convolution factor ofG#x002A;H but neither ofG nor ofH. In contrast,ℱ is known to possess many irreducible elements.
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Ruzsa, I.Z., Székely, G.J. No distribution is prime. Z. Wahrscheinlichkeitstheorie verw Gebiete 70, 263–269 (1985). https://doi.org/10.1007/BF02451431
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DOI: https://doi.org/10.1007/BF02451431