Abstract
The concepts of class L measures and selfdecomposable measures are generalised from vector spaces to simply connected nilpotent groups G. It has been shown that any full class L (probability) measure μ on G can be decomposed as μ = μ 1* ... *μ n, where each μ i is a selfdecomposable measure on a subgroup G i; μ itself is selfdecomposable under certain additional conditions—for example, when μ is symmetric. This generalizes a well known result on vector spaces. Some examples of class L measures on G are also constructed.
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Shah, R. Selfdecomposable Measures on Simply Connected Nilpotent Groups. Journal of Theoretical Probability 13, 65–83 (2000). https://doi.org/10.1023/A:1007778725065
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DOI: https://doi.org/10.1023/A:1007778725065