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What do you mean there is no uniform distribution over any infinite set? There is the uniform distribution over [0,1] which is both infinite and not even count
by x0x0 12y ago
What do you mean there is no uniform distribution over any infinite set? There is the uniform distribution over [0,1] which is both infinite and not even countable.
I'm confused.
- xxxyy 12y agoI meant a distribution with "discrete" probability, i.e. a distribution where the probabilities of singletons are all equal and nonzero, so that a simple Bayesian argument could possibly be extended. My bad for not being precise enough. Perhaps I should have stuck to natural numbers in my previous comment, otherwise yes, you can have uniform distributions with respect to some additional structure of the probability space (like [0,1] with the Lebesgue measure you suggest).