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So I recently came across this question, where the OP asks for a proof of the uniform convergence of a certain sequence, and I happen to have a link to some lecture notes which contain a detailed proof of (a slightly more general version of) the result the OP asked about.

I now wonder what is MSE's community consensus on the appropriate course of action to take in this situation : From the related Meta posts I've found (post 1, post 2), it seems that giving an appropriate link with enough context is acceptable as an answer, or otherwise as a comment. I am just not really clear of what amount of context would be deemed as "enough".

I thus ask, out of these options, which one would be considered best ? :

  1. Writing as a comment :

you can find the detailed proof of this result on page 2 of these lecture notes [link to lecture notes]

  1. Writing as an answer :

The detailed proof of this result can be found on page 2 of these lecture notes [link to lecture notes].
The idea of the proof is to [explanation of the proof main ideas e.g. : "cover the compact set $\Theta$ by a finite number of balls of radius $\varepsilon$, then use the union bound over these balls together with WLLN and continuity arguments to get your result"]

  1. Writing as an answer :

The detailed proof of this result can be found on page 2 of these lecture notes [link to lecture notes]. In order to make this answer self-contained, I reproduce the proof (not mine) below :
[detailed proof of the result as in the linked lecture notes]

To me, option 1 does not make sense : the linked resource effectively answers the question, so it has to be given as an answer. However I feel like a case could be made for both options 2 and 3 (or even others I haven't considered), so I would like to know the community's consensus on this.

P.S.: I am aware the question I linked to has already been answered, I am asking for future reference.

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    $\begingroup$ I think I would argue that picking between 2 & 3 depends on the chances of link rot. If you're using an argument from a published paper, the arXiv, or some other resource which is unlikely to move over the years, 2 can be a good idea. But if you're using an argument from a grad student or postdoc's notes on their personal website, those things can move relatively often and it might be better to reproduce the whole thing. $\endgroup$
    – KReiser
    Feb 4 at 19:10
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    $\begingroup$ You're right that option 1 is not viable, since it forces people to go elsewhere, and that place may no longer exist tomorrow - they came to Math SE for a reason. Option 2 would be acceptable, if somewhat incomplete, it's certainly better than the posts that consist of "Hint:" followed by a single idea. Option 3 is great, if you want to make the effort of transcription and give credit as appropriate (giving the the link and naming the author should suffice). $\endgroup$
    – Nij
    Feb 4 at 23:36
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    $\begingroup$ Your options are well thought out; we appreciate your assessment of options. I think the only thing I'd say is not to post "See [this link](URL)" as an answer. But you clearly have not proposed that as an option. A comment might be good below a question, if you know a standard text (or own it), where the problem occurs and includes proof. If the question is tagged "reference request", than feel free to answer with a reference, and briefly summarize. $\endgroup$
    – amWhy
    Feb 8 at 15:49
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    $\begingroup$ Like Nij, I think option 3 is the best if you can be bothered. A thought occurs, though: are there potential copyright issues, reproducing a proof from a paper or lecture notes, without permission, under a Creative Commons license? It's never stopped me before, but that's the only potential downside to option 3. $\endgroup$ Feb 9 at 1:24
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    $\begingroup$ @Theo Yes, there are copyright & licensing issues. Anyone can copy material from this site (if they give proper attribution), so any material you publish here must be either your own work, or work that (somehow) gives explicit permission to distribute it under the conditions of the CC-BY-SA license. I should be able to copy material from your posts, confident that I am not infringing copyright or license conditions. $\endgroup$
    – PM 2Ring
    Feb 9 at 17:56
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    $\begingroup$ If you are going to use a link to a published research paper, please use a DOI link rather than a direct link to a publisher's website. This helps to prevent link rot. $\endgroup$ Feb 12 at 18:59

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