A note on conservative measures on semigroups

N. A. Tserpes

International Journal of Mathematics and Mathematical Sciences, 1992, vol. 15, 1-4

Abstract:

Consider ( S , B , μ ) the measure space where S is a topological metric semigroup and μ a countably additive bounded Borel measure. Call μ conservative if all right translations t x : s → s x , x ∈ S (which are assumed closed mappings) are conservative with respect ( S , B , μ ) in the ergodic theory sense. It is shown that the semigroup generated by the support of μ is a left group. An extension of this result is obtained for σ -finite μ .

Date: 1992
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DOI: 10.1155/S016117129200022X

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