1
vote
1answer
33 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 ...
3
votes
2answers
118 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 ...
0
votes
2answers
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
1
vote
1answer
275 views

About the measurable subsets and the Lipschitz condition

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. ...
1
vote
0answers
84 views

About Lebesgue measure

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 ...