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Journal of the London Mathematical Society 1994 50(3):417-429; doi:10.1112/jlms/50.3.417
© 1994 by London Mathematical Society
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© The London Mathematical Society

Measures on the Random Graph

Michael H. Albert

Department of Mathematics, Carnegie Mellon University Pittsburgh, Pennsylvania 15213, USA

Received 13 July 1992. Revision received 19 May 1993.

We consider the problem of characterizing the finitely additive probability measures on the definable subsets of the random graph which are invariant under the action of the automorphism group of this graph. We show that such measures are all integrals of Bernoulli measures (which arise from the coin-flipping model of the construction of the random graph). We also discuss generalizations to other theories.


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