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Krengel–Lin decomposition for probability measures on hypergroups

✍ Scribed by C.Robinson Edward Raja

Publisher
Elsevier Science
Year
2003
Tongue
French
Weight
100 KB
Volume
127
Category
Article
ISSN
0007-4497

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✦ Synopsis

A Markov operator P on a σ -finite measure space (X, Σ, m) with invariant measure m is said to have Krengel-Lin decomposition if

and Σ d is the deterministic σ -field of P . We consider convolution operators and we show that a measure λ on a hypergroup has Krengel-Lin decomposition if and only if the sequence ( λn * λ n ) converges to an idempotent or λ is scattered. We verify this condition for probabilities on Tortrat groups, on commutative hypergroups and on central hypergroups. We give a counter-example to show that the decomposition is not true for measures on discrete hypergroups.

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