# Understanding the Dirac Delta function

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## Main Question or Discussion Point

I just want to make sure that I am understanding the Dirac Delta function properly. Is the following correct?:

For two variables $x$ and $y$:

\begin{split}
\delta(x-y) f(x) &= f(y)
\end{split}

And:

\begin{split}
\delta(x-x) f(x) &= f(x)
\end{split}

Staff Emeritus
2019 Award
Neither of those is correct.

Ssnow
Gold Member
The Dirac delta is not a function in the traditional sense, it can be rigorously defined either as a distribution or as a measure.
Ssnow

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