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Jun 15, 2017 at 21:38 comment added Christian Remling An afterthought: A general obstacle to the property that you were hoping for is that often it will imply that $S$ is compact (because $S-S_n$ frequently is, for example in my example), so if this is false, your property can't hold. (Parts of my answer could be rephrased in those terms.)
Jun 15, 2017 at 0:41 vote accept BaoLing
Jun 15, 2017 at 0:26 answer added Christian Remling timeline score: 1
Jun 14, 2017 at 23:20 comment added Anthony Quas I think your monotonicity condition implies that there exists a decreasing function $f$ so that $K(x,y)=f(\|(x,y)\|)$.
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Jun 14, 2017 at 21:24 history asked BaoLing CC BY-SA 3.0