As a problem I was asked to show that phi, as defined by:(adsbygoogle = window.adsbygoogle || []).push({});

[tex]\phi_n(t) = \frac{n}{\pi(1+n^2t^2)}[/tex]

Satisfies the property that for any f with the property to continuious at 0, then:

[tex]\lim_{n\rightarrow\infty} \int_{-\infty}^{\infty} \phi_n(t)f(t)dt = f(0)[/tex]

But if we let f be 1/phi, we see that it is continuous, but f(0) = 0 and the above integral is infinity.

Is this a valid counterexample?

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# Delta sequences

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