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WROCŁAW UNIVERSITY
OF SCIENCE AND
TECHNOLOGY

Contents of PMS, Vol. 25, Fasc. 1,
pages 155 - 171
 

FUNCTIONAL LIMIT THEOREMS FOR PROBABILITY MEASURES ON HYPERGROUPS

Sonja Menges

Abstract: Let K be a hypergroup with left Haar measure and (n ) n a sequence of symmetric probability measures on K converging to e . e We will prove a functional limit theorem in the sense that convergence nkn--> m (- M1(K) n implies unique embeddability of m into a symmetric convolution semigroup (mt)t>0 and [knt] nn --> mt holds for all t > 0. This generalizes the corresponding result for hermitian hypergroups. Furthermore, by analogy with locally compact groups, it can be shown that for specific hypergroups similar results are available without symmetry assumptions.

2000 AMS Mathematics Subject Classification: 43A62, 60B10, 60B15, 60E07, 60G51.

Key words and phrases: Hypergroups, functional limit theorem, infinitely divisible laws, embedding.

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