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Feb 26, 2019 at 20:22 comment added user44143 Another open question: does every subinterval of [0,1] have positive probability?
Feb 26, 2019 at 16:04 comment added user114668 FWIW the family of distributions I was thinking about is something like $\bigl(x^2 (1-x)^2 (1-2x)^2\bigr)^{-t}$ near $t=1/2$.
Feb 25, 2019 at 17:29 comment added user114668 I think an interesting question here is what property i) makes this $f$ (and its square and cube) have discontinuous parts, ii) makes $f$ have also a continuous part, but iii) makes e.g. $f = xyz$ have no point mass (but what seems like a funky distribution)? Edit: Actually I think it is not even clear that these are discontinuities.
Feb 25, 2019 at 16:56 history edited user44143 CC BY-SA 4.0
put lemma up front, since it is an easy introduction to some of the notation, and it reduces the heavy numbering
Feb 25, 2019 at 16:36 history edited user44143 CC BY-SA 4.0
small formatting edits
Feb 25, 2019 at 15:05 history answered Jairo Bochi CC BY-SA 4.0