Invariant measures concentrated on countable structures

@article{Ackerman2016InvariantMC,
  title={Invariant measures concentrated on countable structures},
  author={Nathanael Ackerman and Cameron E. Freer and Rehana Patel},
  journal={Forum of Mathematics, Sigma},
  year={2016},
  volume={4}
}
  • Nathanael Ackerman, Cameron E. Freer, Rehana Patel
  • Published 2016
  • Mathematics
  • Forum of Mathematics, Sigma
  • Let L be a countable language. We say that a countable innite L-structure M admits an invariant measure when there is a probability measure on the space of L-structures with the same underlying set as M that is invariant under permutations of that set, and that assigns measure one to the isomorphism class of M. We show that M admits an invariant measure if and only if it has trivial denable closure, i.e., the pointwise stabilizer in Aut( M) of an arbitrary nite tuple of M xes no additional… CONTINUE READING

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