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They say:

For the kernel function [itex]K_{\delta}(x)=\frac{1}{\sqrt{2 \pi \delta}} e^{-\frac{x^2}{2 \delta}}[/itex] for [itex]\delta>0[/itex],

we have as [itex]\delta \rightarrow 0+ , K_{\delta}(x)= \infty[/itex] if [itex]x=0[/itex] and [itex]K_{\delta}(x)= 0[/itex] if [itex]x \neq 0[/itex].

therefore [itex]\lim_{\delta \rightarrow 0} K_{\delta}(x)[/itex] does not exist.

doesn't this contradict itself? it says the limit doesn't exist but in the line before it just said what the limit was?