A Cauchy Distribution is a perfectly valid probability distribution, but has an undefined meanpic.twitter.com/eNMBzSeGa6
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I don't think "→∞" is the right way to say what goes wrong with this integral. You can find open sets U_i whose union is the real line such that the integral of this function over U_i approaches *whatever you want* - any finite number, or +∞, or -∞ - or doesn't converge.
that's a good point.. i was worrying about that after i saw @AndrewM_Webb 's animation
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Us math types would just say this function is not Lebesgue integrable.
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