/sci/ - Science & Math

>>6600509
What do you find to be difficult about it?

>>6600509
What textbook/notes are you using?

/sci/ will never admit anything is hard.

>>6600513

i can give you an example:

look at the set A (pic related). Now the task is to calculate the volume of this set with the lebesgue measure. in fact it's a very simple set and i'd simply calculate volume =1 (for it's a geometric series of intervalls with the length 1/2^m). But according to my tutor, this is absolute bullshit and you are supposed to calculate it by first setting a "lower limit" and then setting an "upper limit" for the volume and then using limits (for certain elements appraching 0) to show that upper limit = lower limit = 1. I just dont understand this whole procedure. why so complicated? I got the exact same result and yet it's wrong? Wtf.

But i have to admit: even tho measure theory is (apparantly) quite difficult, i enjoy thinking about these kind of problems. I just wonder why it's so hard.

>>6600526

I am using a german textbook (Jürgen Elstrodt - Maß- und Integrationstheorie).

>>6600538

Well i guess i just did.

>>6600547
I'd be interested in seeing this problem worked out too if any anon has the time.

>>6600547
Have you proved that the Lebesgue measure is a countably additive measure that assigns to each interval of R its length?

>>6600557

Ha! That's exactly the point! I KNOW that the lebesgue measure assigns to each interval its length, but we only proved this for half-open intervals (a,b]. So the idea was basically: How can i prove that volume((a,b])=volume([a,b]).

This is exactly that kind of shit i dont understand. I mean, isn't it trivial that volume((a,b])=volume([a,b])?

>>6600557

and yea, we proved that it's countably additive

>>6600564
Have you proved that it is 'monotone', in the sense that if A is contained in B, then the measure of A is less than B? This is actually trivial, from the definition. I'll work under the assumption that you did.

So you know that volume((a,b]) = b-a, and you want to know volume([a,b]). Well, for each s > 0, (a-s,b] has the measure b-a+s, and it contains [a,b], so volume([a,b]) <= volume((a-s,b]) = b-a+s for all s > 0. Hence volume([a,b]) <= b-a by letting s go to zero. Now do the same trick 'from the inside', letting (a+s,b] be contained in [a,b].

>>6600571

Holy shit you are a genius. You just explained to me with a single post how that shit works. Thanks a lot. Do you study math as well? If so, how did you manage to pass measure theory? Any tips?

>>6600584
Yea, I study maths. What's on your course syllabus?

>>6600596

Lebesgue measure
Lebesgue integrals
convergence criteria (Levi, Fatou, Lebesgue)
L^p-Rooms
Fubini
Transformation of Lebesgue integrals
Hausdorff paradoxon
differentiable manifolds

and then random stuff like Rham-Cohomologies, Gauß integral theorem, Stokes theorem etc.

>>6600571

wow, nice trick m8

I love math, it's all about the right trick

>>6600613
Well all I can say is that the first 5 items are absolutely fundamental to almost any further work in analysis. Good luck with the course.

>>6600642
Thanks, but there are other ways, all depends on what kind of facts OP has available to him. If one knows that the measure is additive and that singletons have zero measure, then one can also see this from
volume([a,b]) = volume({a}) + volume((a,b]) = b-a. In any case, the trick of approximating 'from the inside' and 'from the outside' is important.

>>6600513
>want to learn measure theory
>need set theory. no explanation
>need logic notation. no explanation
There's some implicit assumption that readers were supposed to know this beforehand, but no one ever cares about the grit. You can learn everything but notation is foreknowledge of the true world unbegotten of your soul as a fragment of God's mind.

Being born a blank slate is suffering.

>>6600673
>need set theory. no explanation
Skim the UTM text called Naive Set Theory. You probably don't need axiomatic set theory for this.

>>6600547
Your tutor is wrong, you are right for measuring the volume of THAT set. However it seems from the pic that you're trying to prove that the rationals are a null set.

For many sets you're tutor is sorta right about how to find the volume. You're more likely to prove that the volume is between n-\epsilon and n_\epsilon for all \epsilon.

>>6600564
No, it's not trivial. It needs to be proven, but it's very easy to do.

>>6600571
Yes, that's how you do it. You'll use this method a lot.

Here's a fantastic resource for measure theory. It doesn't just stick with Lebesgue measure so if that's difficult for you than you won't like it. However, if you're comfortable working over an arbitrary measure space it proves everything so beautifully, is an easy read, and you will get familiar with the common methods used.

http://math.berkeley.edu/~rieffel/measinteg.html

It isn't. If you're too untalented for basic math, then drop out.

>>6601252

>measure theory
>basic math

This isn't linear algebra, son.

>>6600547
>I am using a german textbook (Jürgen Elstrodt - Maß- und Integrationstheorie).
Try Folland's Real Analysis.

>>6601408
It's even simpler than linear algebra.

>>6601448

I really doubt you ever tried to work differentiable manifolds or lebesgue integral transformation (or you just find linear algebra extremely difficult)

>>6601448
Which is even simpler than interuniversal teichmuller theory!
Am i patrician yet?

>>6601468
I'll repeat it once again: If second semester math is too hard for you, then consider dropping out. Be thankful that it's taught that early, so you didn't waste too much time studying a subject you are untalented in.

>>6601469
Bitch please. I have a PhD in triple integrals.

>>6601475
Good one, you add real value to this board

>>6601477
thank you

>>6601471
Wat

>>6601483
you are welcome sir! Enjoy your compliment

>>6601485
OP is crying about mandatory basics being too hard. This is the wrong attitude in math.

>>6600547
>I got the exact same result and yet it's wrong? Wtf.
that's a VERY retarded thing to say when you do math, dude.

>>6601252
>>6601448
>>6601471
>>6601488

How is your life?

>Ooops sorry, you don't have one.

>>6601471
Not every university covers the same material in measure theory courses nor do they cover them at the same level. My university throws the basics into analysis and the actual measure theory course is graduate level.

>>6601725

same here. Measure theory =/= calculus basics

>>6601488

I never cried about it. in fact i even mentioned in my post >>6600547 that i enjoy studying measure theory and I'm just wondering why i am having such a hard time doing it.

You must be quite an extraordinary autist my friend.

>>6601698
My life is great. Thanks for asking. Why are you projecting your insecurities into me?

>>6601725
So what? It's still an easy subject.

>>6602158
>Why are you projecting your insecurities into me?
Because we're the same person, Tyler.

this thread makes me a sad panda :(

>>6602158
It means you're full of shit. My guess is probably an undergrad or engineer.

First good thread I've seen on /sci/ since 2011. Congratulations OP. Measure theory isn't that hard, you just don't quite have the hang of it yet.

>>6602158
get the fuck out faggot

yeah I'm starting grad school in the fall and need to take a class called "Measure & Integration" which I guess is measure theory and analysis, shit looks pretty fucking scary, I barely got a B in undergrad analysis and that was over a year ago, shit is gonna wreck me. worst part is I need to pass a fucking PhD qualifier based on the course at the end of the year to progress...fuck.

Anyone got any advice for how to prepare for this kind of class other than reading over baby rudin? the berkeley class notes link looks way too hard for something I'm doing a few hours a week at night after working my internship

>>6602623
the big difficulty with measure theory as it is encountered at college is the big jump in abstraction in combination usually with the general lack of discussion around integration in babby real analysis courses.

for preparation, being comfortable with how abstract mathematics works from topology and algebra are better than hammering through analysis texts imo, as these usually take the same dry approach no matter whose teaching it. stick to the definitions and keep a good set of examples at hand rather than relying too much on past analysis/calc experiences.

>>6602590
You guessed wrong. Try again.

>>6602623
You want to go for a PhD and you're scared by an introduction to a very intuitive undergrad subject? I call bullshit. I dare you to show me one thing you consider "hard" in measure theory.

>>6602193
Haha, I remember that movie. The director most certainly is a /b/tard. Did you notice how he took /b/'s rule "Do not talk about /b/" and replaced "/b/" with "fight club"?

>>6603091
>futuramafry.jpg
The movie, and the book it was adapted from, predate 4chan.

>>6603091
>Haha, I remember that movie. The director most certainly is a /b/tard. Did you notice how he took /b/'s rule "Do not talk about /b/" and replaced "/b/" with "fight club"?
you're so subtlety ironic, aren't you

Anyway,
the movie Fight Club was released in 1999, adapted from the eponymous book published in 1996.

4chan was created in 2003, and the so called "rules of internet" were written in early 2007.
It was a cool dicussion
http://web.archive.org/web/20070110035128/http://www.encyclopediadramatica.com/index.php/Rules_Of_The_Internet

------


For measure theory, I used to refer to Terrence Tao notes (http://terrytao.files.wordpress.com/2011/01/measure-book1.pdf))

As a nice introduction (easy to read, lots of example/drawings), I would recommend the short
http://www.yetanotherquant.de/yetanotherbook/chapter2/chapter2.pdf

>>6603101
(i don't think he was being entirely serious)