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Aug 31, 2020 at 15:58 comment added DCM Just for me (and others reading this), would you mind making your hypotheses concerning $X$, $Y$, $f$ and $g$ a little clearer? Is your hypothesis that $X$ and $Y$ are such that there is a $p>2$ such that $f(X), g(Y)\in L^p$ and (1) holds for all Lipschitz $f$ and $g$, or something else?
Aug 31, 2020 at 12:13 comment added Robert W. That's because (1) need not hold for $cX$ and $cY$.
Aug 31, 2020 at 11:13 comment added DCM Re. I don't see where my logic fails, why do you think it does?
Aug 31, 2020 at 10:38 comment added Robert W. The hypothesis in (1) implies (2) and (4), and (2) supposedly implies (3). I don't see where my logic fails.
Aug 31, 2020 at 9:52 history answered DCM CC BY-SA 4.0