A doubt: With Lebesgue measure, $\int_{\mathbb{R}\setminus \left\{0\right\} } \frac{1}{x^2}dx$ converges?


closed as off-topic by Saad, RRL, max_zorn, eyeballfrog, Cesareo Jan 12 at 8:01

This question appears to be off-topic. The users who voted to close gave this specific reason:

  • "This question is missing context or other details: Please provide additional context, which ideally explains why the question is relevant to you and our community. Some forms of context include: background and motivation, relevant definitions, source, possible strategies, your current progress, why the question is interesting or important, etc." – Saad, RRL, max_zorn, eyeballfrog, Cesareo
If this question can be reworded to fit the rules in the help center, please edit the question.

  • 1
    $\begingroup$ Can't this be decided just using improper Riemann integral on $(0,1)$? [We have an antiderivative $-1/x$ which when evaluated from $a$ to $1$ and then make $a \to 0^+$ diverges.] $\endgroup$ – coffeemath Jan 12 at 4:01