(Semi-) stability and limit theorems on general locally compact groups

Multiple decomposability of probabilities on contractible locally compact groups

“…Then there exist a group of dilations (δ t ) with τ δ t = δ t τ for all t. (Cf. e.g., [7], Remark 2.1.13 a)). Let | · | denote a (sub-additive homogeneous) norm adapted to the dilations.…”

“…This generalizes e.g., [6], Proposition 3.4, Theorem 3.5, resp. [7], Proposition 2.14.24, for the case n ≥ 0. In particular this proves that P log n+1 + does not depend on the particular chosen group norm.…”

“…In fact, in [30], 3.7, [7], 3.2.8, it is supposed that p is a prime power, hence Q p a field. But the construction does not depend on this assumption.…”

“…[6], [7]) we define logarithmic moments in terms of group norms. (For vector spaces see e.g., [11].)…”

“…Recall that for non-Abelian groups, generating functionals of continuous convolution semigroups play the role of logarithms of Fourier transforms, the second characteristic functions. For details the reader is referred to, e.g., [10], Ch IV, § 2.0, [7], [29], [3].…”