MixedNuts comments on St. Petersburg Mugging Implies You Have Bounded Utility - Less Wrong
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Assigning zero probability to claims is bad because then one can't ever update to accept the claim no matter what evidence one has. Moreover, this doesn't seem to have much to do with "infinite claims" given that there are claims involving infinity that you would probably accept. For example, if we got what looked like a working Theory of Everything that implied that the universe is infinite, you'd probably assign a non-zero probability to the universe being infinite. You can't assign all hypotheses involving infinity zero probability if you want to be able to update to include them.
The hypothesis that the universe is infinite is equivalent to the hypothesis that no matter how far you travel (in a straight line through space), you can be infinitely certain that it won't take you someplace you've been. Convincing you that the universe is infinite should be roughly as hard as convincing you that there's zero probability that the universe is infinite, because they're both claims of infinite certainty in something. (I think.)
I'd like to be able to boil that down to "infinite claims require infinite evidence", but it seems to be not quite true.