No distribution is prime |
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| Authors: | I. Z. Ruzsa G. J. Székely |
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| Affiliation: | 1. Mathematical Institute of the Hungarian Academy of Sciences, Budapest, Hungary
2. Mathematical Institute, Department of Probability Theory, E?tv?s Loránd University, H-1088, Budapest, Hungary
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| Abstract: | 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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