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The embedding problem for probabilities on locally compact groups. (English) Zbl 1145.60006

Dani, S. G. (ed.) et al., Probability measures on groups: recent directions and trends. Proceedings of the CIMPA-TIFR school, Mumbai, India, September 9–22, 2002. New Delhi: Narosa Publishing House/Published for the Tata Institute of Fundamental Research (ISBN 81-7319-703-2/hbk). Studies in Mathematics. Tata Institute of Fundamental Research 18, 331-363 (2006).
The paper contains notes from a lecture course on classes of locally compact groups, on which any infinitely divisible measure can be embedded into a continuous one-parameter semigroup of measures. The author presents proofs of the embedding results for \(p\)-adic linear groups, discrete real linear groups, and connected coverings of linear real Lie groups. Possible generalizations to measures on semigroups are discussed. The author gives complete references regarding the above results, at the same time recommending to a reader his introduction to the subject: Expo. Math. 26, 147–164 (1998; Zbl 0908.43002).
For the entire collection see [Zbl 1130.60006].

MSC:

60B15 Probability measures on groups or semigroups, Fourier transforms, factorization
28C10 Set functions and measures on topological groups or semigroups, Haar measures, invariant measures
43A05 Measures on groups and semigroups, etc.

Citations:

Zbl 0908.43002
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