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1. • CommentRowNumber1.
   • CommentAuthorUrs
   • CommentTimeSep 6th 2017
   • (edited Sep 6th 2017)
   • PermaLink
   Author: Urs
   Format: MarkdownItexI have added to _[[step function]]_ statement and proof of its representation as $$ \begin{aligned} \Theta(x) & = \frac{1}{2\pi i} \int_{-\infty}^\infty \frac{e^{i \omega x}}{\omega - i 0^+} \\ & \coloneqq \underset{ \epsilon \to 0^+}{\lim} \frac{1}{2 \pi i} \int_{-\infty}^\infty \frac{e^{i \omega x}}{\omega - i \epsilon} d\omega \,, \end{aligned} $$ ([here](https://ncatlab.org/nlab/show/step+function#FourierIntegralFormula)).

   I have added to step function statement and proof of its representation as

   $$\begin{aligned} \Theta(x) & = \frac{1}{2\pi i} \int_{-\infty}^\infty \frac{e^{i \omega x}}{\omega - i 0^+} \\ & \coloneqq \underset{ \epsilon \to 0^+}{\lim} \frac{1}{2 \pi i} \int_{-\infty}^\infty \frac{e^{i \omega x}}{\omega - i \epsilon} d\omega \,, \end{aligned}$$

   (here).

2. • CommentRowNumber2.
   • CommentAuthorUrs
   • CommentTimeSep 6th 2017
   • PermaLink
   Author: Urs
   Format: MarkdownItexWhile I was it, I also added statement and proof that $\partial \Theta = \delta$ (copied that also over to the Properties-section of _[[delta distribution]]_ and to the Examples-section at _[[derivative of distributions]]_).

   While I was it, I also added statement and proof that $\partial \Theta = \delta$ (copied that also over to the Properties-section of delta distribution and to the Examples-section at derivative of distributions).

3. • CommentRowNumber3.
   • CommentAuthorDavidRoberts
   • CommentTimeSep 6th 2017
   • PermaLink
   Author: DavidRoberts
   Format: MarkdownItex[[step function]] (typo in your link)

   step function (typo in your link)

4. • CommentRowNumber4.
   • CommentAuthorUrs
   • CommentTimeSep 6th 2017
   • PermaLink
   Author: Urs
   Format: MarkdownItexThanks, fixed now.

   Thanks, fixed now.