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Sep 2, 2022 at 3:51 comment added Nate River It should be said that if the probability density function $f$ is continuous or smooth, then it’s value at a point actually matters - since it guarantees that nearby values are close even if you modify $f$ on a set of measure $0$. In that case arguing based on pointwise values would not be bad form.
Sep 2, 2022 at 3:33 history answered Timothy Chow CC BY-SA 4.0