Re: Lebesgue measure on RxR

(i) You computed the measure of the triangle whose vertexes are , , , but it's not what it's asked. You can write and show that for all , . To do that, you can cover the line for a fixed by squares with measure .

(ii) Write where . We can compute the measure of the complement of in writing .

Re: Lebesgue measure on RxR

(i) Oh, I see. And then one lets and we obtain and since the original set is a disjoint union of sets of measure zero we get at it is also of measure zero.

(ii) Here I fully understand what you mean but I'm not sure of my result.

So what I get is . And then . So .

Is this correct? What I'm not sure about is the step , from what I've read the set needs to be a "rectangle" for that to be allowed.

Re: Lebesgue measure on RxR

(i) It's ok.

(ii) We can write, since the measures of the following sets are finite: , and conclude since is countable.