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The Action of a Solvable Group on an Infinite Set Never has a Unique Invariant Mean
1988
Transactions of the American Mathematical Society
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Theorem 1 of the paper proves a conjecture of J. Rosenblatt on nonuniqueness of invariant means for the action of a solvable group G on an infinite set X. The same methods used in this proof yield even a more general result: Nonuniqueness still holds if G is an amenable group containing a solvable subgroup H such that card(G/H) < caid(H).
doi:10.2307/2001058
fatcat:c2hg4zsjordiladmqbrw7a6fli