Amenability, Reiter’s condition and Liouville property. (English) Zbl 1509.22002
Summary: We show that the Liouville property and Reiter’s condition are equivalent for semigroupoids. This result applies to semigroups as well as semigroup actions. In the special case of measured groupoids and locally compact groupoids, our result proves Kaimanovich’s conjecture of the equivalence of amenability and the Liouville property.
MSC:
| 22A22 | Topological groupoids (including differentiable and Lie groupoids) |
| 43A05 | Measures on groups and semigroups, etc. |
| 43A07 | Means on groups, semigroups, etc.; amenable groups |
| 45E10 | Integral equations of the convolution type (Abel, Picard, Toeplitz and Wiener-Hopf type) |
| 46E27 | Spaces of measures |
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