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Nov 11, 2015 at 13:02 comment added Pietro Majer Yes, that's ok, but as it was stated, in the case $t=T$ we couldn't deduce that a finite family of balls covers $(t',t] \times B_r$ for some $t'<t$ (it should only be true "countable").
Nov 11, 2015 at 11:01 history bounty ended zhoraster
Nov 11, 2015 at 11:01 comment added zhoraster I think there was no problem with the former argument, as $T$ belonged to $I$ obviously: the set $(t,T)\times B_r$ is empty for $t=T$.
Nov 11, 2015 at 6:41 comment added Pietro Majer A minor correction was needed: the sentence after "Notice that" is not true for $t=T$, because $\{T\}\times B_r$ is not contained in $\mathbf{S}$ and shouldn't be covered by $\mathsf{D}$. I slightly modified the argument correspondingly.
Nov 11, 2015 at 6:35 history edited Pietro Majer CC BY-SA 3.0
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Nov 11, 2015 at 4:07 vote accept zhoraster
Nov 10, 2015 at 22:55 history edited Pietro Majer CC BY-SA 3.0
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Nov 10, 2015 at 22:49 history edited Pietro Majer CC BY-SA 3.0
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Nov 10, 2015 at 22:39 history edited Pietro Majer CC BY-SA 3.0
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Nov 10, 2015 at 22:25 history edited Pietro Majer CC BY-SA 3.0
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Nov 10, 2015 at 22:17 history edited Pietro Majer CC BY-SA 3.0
deleted 5 characters in body
Nov 10, 2015 at 21:27 history answered Pietro Majer CC BY-SA 3.0