- #1
psie
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- TL;DR Summary
- I'm stuck at something fairly basic I think. Let
be an open ball of radius and center in . It is claimed that pointwise as and on , where is the sphere . I am stuck showing this.
I'm reading a proof of a lemma that where is Lebesgue measure, is jointly continuous in and ( stands for average). The claim that on is made in the proof. I think there are two cases to consider. Let .
on the sphere ?
, i.e. . Is it then also true that for some sequences that converge to respectively, that for large enough ? Why? If yes, then for large enough too.- Similarly, if
, is it then true that ?