Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Invariant measures concentrated on countable structures   Let L be a countable language. We say that a countable infinite 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
definable closure, i.e., the pointwise stabilizer in Aut(M) of an arbitrary
finite tuple of M fixes no additional points. When M is a Fraisse limit in a
relational language, this amounts to requiring that the age of M have strong
amalgamation. Our results give rise to new instances of structures that admit
invariant measures and structures that do not.

26
The categories of this paper are: bayes-an
16
The categories of this paper are: stat
0
The categories of this paper are: hep-ph
34
The categories of this paper are: chem-ph
18
The categories of this paper are: econ
17
The categories of this paper are: q-fin
8
The categories of this paper are: hep-ex
21
The categories of this paper are: adap-org
19
The categories of this paper are: eess
7
The categories of this paper are: hep-th
3
The categories of this paper are: physics
35
The categories of this paper are: mtrl-th
10
The categories of this paper are: q-bio
32
The categories of this paper are: atom-ph
22
The categories of this paper are: chao-dyn
25
The categories of this paper are: patt-sol