Abstract
Let G be a connected reductive Lie group and K be a maximal compact subgroup of G. We prove that the semigroup of all K-biinvariant probability measures on G is a strongly stable Hungarian semigroup. Combining with the result [see Rusza and Szekely(9)], we get that the factorization theorem of Khinchin holds for the aforementioned semigroup. We also prove that certain subsemigroups of K-biinvariant measures on G are Hungarian semigroups when G is a connected Lie group such that Ad G is almost algebraic and K is a maximal compact subgroup of G. We also prove a p-adic analogue of these results.
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Raja, C.R.E. On a Class of Hungarian Semigroups and the Factorization Theorem of Khinchin. Journal of Theoretical Probability 12, 561–569 (1999). https://doi.org/10.1023/A:1021642531006
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DOI: https://doi.org/10.1023/A:1021642531006