I've asked this question. Until now, it has 3 votes to close, but I'm having a hard time understanding the reasons given.

What can I do to improve this question?

  • $\begingroup$ I'm not sure if the notation is sufficiently self-explanatory. At first glance I took the hypothesis to be $f,g$ are Borel-measurable in $\mathbb{R}^n$, whereupon you asked what might be the smallest sigma-algebra on $\mathbb{R}^n$ that makes $f-g$ measurable. Apparently (from your doubt about the posted answer) this is not the right understanding. $\endgroup$ – hardmath Jul 26 '17 at 4:19
  • $\begingroup$ @hardmath Sorry for the notation, I mean $f^{-1}(\mathcal{B}(\mathbb{R}^n))\subset \mathcal{A}$. So they are borel measurable. $\endgroup$ – An old man in the sea. Jul 26 '17 at 8:46
  • $\begingroup$ What my doubt says is that in the example we don't have $f^{-1}, g^{-1} \subset (f-g)^{-1}$... $\endgroup$ – An old man in the sea. Jul 26 '17 at 9:00
  • 2
    $\begingroup$ Indeed, at present, the post asks three separate questions, the first one being the least interesting. (Your last comment above, being syntactically incoherent, does not help to understand what you are really after, assuming you know this yourself.) $\endgroup$ – Did Jul 26 '17 at 12:18

I see two issues. First, two of the close votes indicate that the question is missing context. While many (including myself) think this reason for closing is way overused, it wouldn't be hard to say something about where the question came from. Why are studying it? Is it an exercise? If so, in what text? Did you formulate it yourself? If so, how and why?

Also, I notice that you drop a second question almost parenthetically. If it's related, you should explain that clearly. Otherwise, another question is probably more appropriate.


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