Note that it is not correct that I myself was advised not to make major edits. It is simply general policy on StackExchange, and I would assume also here, that you can edit a question to clarify it, but not entirely change a question, especially after the original question has been answered and changing your question would invalidate it.

My source for this policy is this link: https://math.meta.stackexchange.com/questions/20103/is-that-ok-to-modify-a-question-significantly , but there are other sources.

What I personally would recommend is either to change the question body to make clear that there are two unrelated questions being asked or, alternatively, to ask a new question containing your Question 1. Currently the question body is unsolvable as stated because {we cannot define an explicit non-Lebesgue-integrable $\mathcal{G}: \mathbb{R} \rightarrow \mathbb{R}$ without AC}.

Update: sorry, the {bracketed} part is wrong.

Someone on Reddit told me if we used axiom of choice, we could just use the characteristic function of the Vitali set. However, I wanted something more explicit as desribed by the PhD student.

I have made corrections.

clemens‭ According to a user on Reddit, you can't just say "an everywhere surjective function whose Lebesgue measure is undefined on any interval", you have to say "an everywhere surjective function whose Lebesgue pushforward measure is undefined".

How can I put this in a abstract?

bharathk98‭ So you've seriously been pestering a fourth person on this account?

No, a redditor kept calling my work nonsense. Not on this account.

How did you know the redditor and I are arguing? Have you been stalking me?

bharathk98‭ Alright. In what way is he wrong?

(Edit: for context other readers can look at this link.)

(edit: I just made archived copies.)

bharathk98‭ You yourself linked to /u/kuromajutsushi here

I shall not be assisting your pretenses of erudition any further; they appear to have wasted too many people's time already. Good day!

He could be more respecful. He doesn't have to constantly splurge insults!

Trash talk has no place in mathematics.

I never said I was intellectually superior. Did you read the reddit posts!

bharathk98‭, if you don't understand your own question well enough to write a title for it or to make your own critique of proposed titles, you're probably asking questions at the wrong level. I would suggest that rather than trying to crowdsource an answer to an ill-defined question by pitting people from different sites against each other, you work on understanding for yourself the prerequisites of the area which interests you.

u/PeterTaylor I did not intend to pit the users against eachother. I wanted the truth which I won't be able to determine myself (I know my limitations). Clemens was overexaggerating and was disrespecful.