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1:37 AM
D1, D2, D3
D4, D5, D6
D7, D8, D9
2 hours later…
3:24 AM
@JoséCarlosSantos I'm glad too. Take care and see you around!
7 hours later…
6 hours later…
3:43 PM
Hi all. I'm not a member of Maths.SE, but came across the following set of posts which may potentially be considered duplicates:
Q: Upper bound on the integral of a function given the measure of the integration domain

TerranDropLet $(X,\mathcal{M},\mu)$ be a measure space and $f:X\rightarrow\mathbb{C}$ be a measurable function such that $\int_X |f|\; d\mu <+\infty$. I am trying to prove the following result: \begin{equation} \forall \epsilon >0,\exists \delta >0, \forall E\in\mathcal{M}, \mu(E)<\delta\Rightarrow \int_E...

Q: For every $\epsilon>0$ there exists $\delta>0$ such that $\int_A|f(x)|\mu(dx) < \epsilon$ whenever $\mu(A) < \delta$

Block JeongHello all mathematicians!! Again, I am struggling with solving the exercises in Lebesgue Integral for preparing the quiz. At this moment, I and my friend are handling this problem, but both of us agreed this problem is a bit tricky. The problem is following. Let ($X,\mathcal{A},\mu$) be a measu...

Q: Show $\forall \epsilon > 0$ there exists $\delta > 0$ such that $\int_E {|f|d\mu } < \varepsilon $ for all $E\in \cal M$ with $\mu(E) < \delta$

TonyThe problem is Let $(X,\cal M, \mu)$ be a measure space and consider $f\in L^1(X,\cal M, \mu)$. Show that for each $\epsilon > 0$ there exists $\delta > 0$ such that $\int_E {|f|d\mu } < \varepsilon $ for all $E\in \cal M$ with $\mu(E) < \delta$. I can see if $f$ is bounded by some $M$, we...

Q: Find $\delta >0$ such that $\int_E |f| d\mu < \epsilon$ whenever $\mu(E)<\delta$

phenomenalwoman4I am studying for a qualifying exam, and I am struggling with this problem since $f$ is not necessarily integrable. Let $(X,\Sigma, \mu)$ be a measure space and let $$\mathcal{L}(\mu) = \{ \text{ measurable } f \quad| \quad \chi_Ef \in L^1(\mu) \text{ whenever } \mu(E)<\infty\}.$$ Show that fo...

The only difference between the questions appears to be in the assumptions on f: respectively, f measurable with finite absolute integral, f integrable, f in L^1, and f in a space called L(mu). Probably the first three at least are equivalent (in the second one, should the assumption be |f| integrable or is it enough to say f integrable?)
I don't know this site's closing norms, and don't have an account here to vote/flag for closure, but thought I'd put this in front of the people who do. Hopefully this is the right room to do so.
4:16 PM
is it possible to bounty a closed question?
I want to bounty this wrongly closed question of mine math.stackexchange.com/questions/4666486/…
@Koro No, it is not possible.
4 hours later…
8:53 PM
This seems to be something akin to "please solve this open problem for me". I don't know the field well enough to unilaterally close, but I think that others should have a look, and express their opinions. Find a formula for this sequence: $1, 1, 1, 2, 3, 5, 9, 16, 28, 50, 89. . .$‭ - Alpha‭ 2023-03-26 20:24:07Z
1 hour later…
9:57 PM

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