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Mar 21 at 14:44 history edited leo monsaingeon CC BY-SA 4.0
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Mar 21 at 14:05 history edited leo monsaingeon CC BY-SA 4.0
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Mar 21 at 13:54 history edited leo monsaingeon CC BY-SA 4.0
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Mar 21 at 13:47 comment added leo monsaingeon @LunaBelle you're completely right, this is a crucial mistake (that cannot be fixed in any way) and I plead guilty on the charge of wishful thinking. I edited to provide a correct answer, totally different. I'm surprised nobody spotted it before! (including myself)
Mar 21 at 13:44 history edited leo monsaingeon CC BY-SA 4.0
added 2668 characters in body
Mar 21 at 8:49 comment added Luna Belle Thank you. Could you please provide more detailed explanation for how the last inequality is derived? It doesn't seem obvious based on the definition of the Hausdorff distance
Mar 20 at 16:33 comment added leo monsaingeon as a side note: one could argue directly at the level of a minimizing plan $\pi^*$ (rather than for a minimizing sequence $\pi_n$), but I'm not sure everybody would take for granted the existence of such a plan so I thought best using the apprimation trick
Mar 20 at 12:06 history answered leo monsaingeon CC BY-SA 4.0