Mathematics

robjohn

3:58 AM

@Obliv How do you have a $t$ in the limit of integration when $t$ is the variable of integration?

Obliv

it's notational, was trying to get the indefinite integral idk why I wrote it like that @robjohn

some FTC jazz like

Jakobian

6:42 AM

Pitch the Baby

►

one potato two potato

7:35 AM

I just heard a legendary tale of a PDE professor from her student: So one day, one of the students in her analysis class wanted to ask some questions about her work on PDE after the class. But she refused by saying "You'd better not ask me those questions. My first impression of you will get bad."

Soumik Mukherjee

7:51 AM

I wish I could say the same in my interviews

leslie townes

8:30 AM

soumik: ... i mean, you could say the same in your interviews

Asish Mohanty

Hello

imbAF

8:47 AM

can anyone help me with this:
https://math.stackexchange.com/questions/4407959/power-series-identity-proof

Jakobian

9:24 AM

@AsishMohanty hi

psie

9:42 AM

> Definition 4.8 If $f:X\to\mathbb{\overline{R}}$ is a measurable function, then $$\int f \ d\mu=\int f^+ \ d\mu-\int f^- \ d\mu,$$ provided that at least one of the integrals $\int f^+ \ d\mu$,$\int f^- \ d\mu$ is finite. The function $f$ is integrable if both $\int f^+ \ d\mu$,$\int f^- \ d\mu$ are finite, which is the case if and only if $$\int |f| \ d\mu < \infty.$$

> Remark Note that, according to this definition, the integral may take the values $-\infty$ or $\infty$, but it is not defined if both $\int f^+ \ d\mu$,$\int f^- \ d\mu$ are infinite.

I'm confused about this definition. The integral can only take the values positive or negative infinity if one of $\int f^+ \ d\mu$,$\int f^- \ d\mu$ takes one of those values, but then it isn't defined. Shouldn't something that obtains a value be defined?

Thorgott

it is

Jakobian

> but then it isn't defined

it is defined, as those values of $\infty$ or $-\infty$

but we don't call $f$ to be (Lebesgue) integrable in that case

its a difference

psie

right ok, maybe my confusion mislead me, subtle difference there

Jakobian

subtle in the sense that integrable doesn't mean can be integrated, but it means can be integrated with a finite value (i.e. a real number)

Soumik Mukherjee

9:58 AM

@leslietownes 😆😆

Ryder Rude

11:31 AM

anyone want to play this? lichess.org/fLcQScN2

EE18

2:04 PM

Hello @Thorgott , hope all is well. Do you recall a while back we were discussing intervals of R and how they were uniquely identified by their endpoints and whether they contain them?

This is very much not important, but now that I look back at it it seems the claim was only made for nonempty intervals. But why not empty? The empty set would be the unique interval for which $\inf A = \infty$ and $\sup A = - \infty$

John Zimmerman

2:38 PM

Take a disk with a given metric $g,$ $(D^2, g)$ and identify points on $\partial D^2$ by considering the space of lines with the same slope. Choose an element in this space. Ex. take vertical lines through $D^2$. This quotient space is homeomorphic to $S^2$. But what is the quotient metric on this quotient space?

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$Mathematics$ Mathematics