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Old 05-01-2013, 08:24 AM
Elroch Elroch is offline
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Default Re: Q10 higher bound

There is a proviso to my glib claim above that absolutely any subset can be a hypothesis. While this is true when the underlying set is finite or countable, when it is uncountably infinite I believe it only makes sense to have hypotheses which are measurable sets, according to the probability distribution associated with samples.

[Almost anything that makes any sense is likely to satisfy this, but it is not difficult to construct pathological examples even when the sample space is as simple as the unit interval with the uniform distribution].
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