# Tagged Questions

34 views

### One dimensional integrals in Green's theorem

I am trying to understand Green's theorem, but the problem is I don't know what is the definition of the integrals in the theorem. This is the expression that one proves to hold with some assumption ...
121 views

### Banach space integral via defining it in $X^{**}$ and then proving it's in $X$

Vector-valued integration is something I generally try not to think about very much. I have the impression that it can be a sort of "rabbit hole" of a subtlety if one allows it to be. So, I tend to ...
156 views

### Needing an example of one riemann integrable function

This is easy, but I couldn't find some example of a function that is not integrable but its Riemann improper integral exists and is finite
I have, again, a doubt with the measurable subsets. If I have that $T\colon\mathbb{R}^n\longrightarrow \mathbb{R}^n$ is Lipschitz, does $T$ send Lebesgue measurable sets in Lebesgue measurable sets. ...
This is a problem of Lebesgue measure and measure theory specifically. Suppose that $f:\mathbb{R}^2\longrightarrow [0,\infty)$ is measurable. $\Omega_1\subseteq \mathbb{R}^2$ is Lebesgue ...