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Great! Thank you for this very nice clarification and neat example! Just one small detail: should it be $x^*_n = (0,...,0,1,0,...)$ for $n>1$? (maybe I'm not reading the notation properly)
@Deane Yang You'll have to enlighten me about that remark on delta -- in my narrow view, I'm thinking of $\delta$ as a linear functional on $C_c^\infty$
@Willie Wong I see, just to do everything in reverse... my concern was with the initial usage of the $\delta$ (as I've commented above), which I wanted to avoid.
@Deane Yang My concern is due to fact that in that proof (from Wiki page) we start with an integral of $F$ with $\delta$, doesn't that assume that $F$ is a test field?
