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Sep 17, 2019 at 14:52 comment added Yuval Peres @Iosif Yes, there are.
Sep 17, 2019 at 14:24 comment added Iosif Pinelis The integral is $>-\infty$ if $E$ is the Cantor set. Are there compact sets of zero Lebesgue measure that are much bigger than the Cantor set?
Sep 17, 2019 at 14:18 comment added Iosif Pinelis @Dirk : This is what I am thinking about now. :-)
Sep 17, 2019 at 14:16 comment added Dirk You answered the question somehow, but I think the problem occurs where $d(x,E)$ is small, so integrability is still an issue (i.e. the problem is if the integral exists since it may be $-\infty$ )…
Sep 17, 2019 at 13:50 history answered Iosif Pinelis CC BY-SA 4.0