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.
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.