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cumulant-nimbus comments on 0 And 1 Are Not Probabilities - Less Wrong

34 Post author: Eliezer_Yudkowsky 10 January 2008 06:58AM

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Comment author: cumulant-nimbus 11 January 2008 03:40:32AM 2 points [-]

Caledonian: Not wrong. Take the field you're swinging at to be a plane. There are infinitely many points in that plane; that's just the density of the reals.

Now say there is some probability density of landing spots; and, let's say no one spot is special in that it attracts golf balls more than points immediately nearby (i.e. our pdf is continuous and non-atomic). Right there, you need every point (as a singleton) to have measure 0.

Go pick up Billingsley: measure 0 is not the same as impossible nor does it cause any problems.