Why may we assume that each interval in $\mathcal{F}$ is contained in $\mathcal{O}$? What warrants this reduction?
Why is statement (4) true? If $x \in E - \bigcup_{k=1}^n I_k$, then $x \in E$ and $x \notin I_k$ for every $k=1,...,n$. Given some $\epsilon > 0$, there exists $I \in \mathcal{...
Corollary 5: Let $\{f_n\}$ be a sequence of nonnegative integrable functions on $E$. Then
$$\lim_{n \to \infty} \int_E f_n = 0 ~~~~~~(5)$$
if and only if
$$f_n \to 0 \mbox{ in measure on } E \mbox{ and } \{f_n\} \mbox{ is uniformly integrable and tight over } E ~~~~~(6)$$
H...
What do I do with the above two questions? It's been over two weeks and I still haven't received an answer? Can I delete the questions and ask them again?
@user193319 As far as I can tell, this would be against the rules. (Not to mention having too many deleted questions contributes to the possibility of post-ban.)
At the moment I do not have much time to look the questions you linked.
You could offer some bounty, that might help to attract some attention.
And in case you prefer not to spend your reputation points on bounties, I might be willing to add a bounty myself - but only after I look at the question myself in detail. (And as I said, I might be quite busy for approximately week or two.)
