MathDoctorBob - 2011-10-09
Real Analysis: We motivate the idea of measure by considering an example where Riemann integration fails. We save measures for the next video, but consider the definition of measure zero.
Thanks for the kind words! Still a long way to go, but getting there.
Still a glimmer in my eye. I'm hoping to have the resources to do real analysis videos once this semester ends.
I need to figure out the long term plan first. Right now I want to get another class up. If I had unlimited resources, a real analysis playlist would be next.
Hey, Bob! This is Ojas, we met and spoke at the JMM in Atlanta! Your videos are great!
I hear you. One day.
Thank you for breaking this down!
Not yet. I should get accounts for there, arXiv, and MathOverflow, but I can't imagine the ensuing time sink.
This video was great, thank you.
Man
You're really good
Great lesson: very clear, easy to understand, relates back to topics that students understand, and every small detail is covered and correct. I wished I had had you as my measure Theory teacher when I was in grad school :)
It is a convenient description that emphasizes only the topology used. A simple example is the indiscrete topology on R. The only open sets are the empty set and R itself. So the Borel sets are the empty set and R itself. Any open interval is not Borel (for this topology). For something more complicated, consider the usual Borel sets on R. A standard exercise is to construct a non-measurable set for Lebesgue measure.
Awesome video! Really clear and easy to understand explanation!
thanks from israel :-)
That would be great if you did a real analysis playlist :D
more video lecture on measure theory,plz sir
You're the man!!
Fantastically clear and cool.
Really great thanks for this!
Your welcome! One day, and that day appears to be far away, I will return tho this playlist.
You're welcome! - Bob
Still hoping for more Dr Bob! mathmonk is well presented but superficial.
@Godisahomo Thanks! We'll see how far I get. - Bob
where is the next video for measurable set?
Incredible video- I watched this because I wasn't sure if I wanted to take the Analysis 3 course at my university, but you have me hyped for measure theory; thank you so much!
It's really awesome!! I want to watch the next video about measure theory but can't find it. Does anyone know?
+Sukwon Lee Can't find it either =(
+Sukwon Lee One day. Priorities getting in the way.
I can't find kantorovitch representation theorem in general measure theory
@MathDoctorBob I like your explanation. It gets more into the idea of why measures are defined the way they are. I think it helps with the understanding.
Is there going to be a playlist for Measure Theory?
This is an excellent video. It helped me passed my Real Analysis qualifier. It took me a while to understand what "almost everywhere" means.
Congrats! Are you done with exams?
Hi! This video introduces the needs of measurable sets very clearly. I hope to see the next videos!
Hi J Kim - Bad news! This video is around where I ran out of time/money for the channel. Maybe one day I'll return to the studio (basement).
PERFECT
Thanks Bob. Hope he's as good as you.
Me too, but I have to use measure theory for my research too. Otherwise I ll be kicked out of my program. Hope you make the videos for measure theory fast enough. Thanks again , Bob.
Do you have a Math.SO account?
@xjuhox Agreed. The challenge is presenting to the general audience. The plan is a short series of videos, finishing with the big three theorems (Monotone Convergence, Dominated Convergence, and Fatou's Lemma). I'd do things differently for a class of math majors. Here I'm aiming for more of a user's guide approach with a focus on motivation and application. - Bob
hot
Check out mathematicalmonk's channel. He has a probability theory playlist with measure theory.
Now. So. So. Now. What is the measure of these words?
What's that wand for? Are you a wizard?
Are measurable function continuous?
Usually, no. Graphs of measurable functions can be full of holes and jumps. A big part of real analysis using nice functions (like continuous) to approximate messy functions (like measurable).
@MathDoctorBob thankyou very much:)
@sunita singh Measure theory is used to generalise the notion of the Riemann integral in order to do analysis on erratic functions that are not well behaved. This means that you should view riemann integration as a subset of lebesgue integration, and as such, the notion of continuity as a much more specific phenomena than any notion related to measure.
hi bobo, how's your day
Fair enough. I am not a "math guy" but measure theory is something I need to understand better as probability only gets me so far in my research.
How can the area of the small intervals on the left of epsilon not cover the rest of the area ??? move epsilon a bit to the right, closer to 1 then obviously it will cover it cuz that area from epsilon towards 0 is bigger.
@Fation Rroni I watched your vid I still dont get the big picture and where does the Reimannian integral fail.And why do we want to have a measure 0 if we wanna measure something that needs a concrete measure.
I am doing finance and I have to learn these stuff, I am having a hard time.
These intervals do not UNION (which we write as U) to form the entirety of the [0,1[ interval. We are missing the irrational numbers. At least that's my understanding.
If we remove the neighborhood of the rationals we still have an interval, composed of the partitions of the irrationals, which is very close to the entire interval [0,1]
In other words, the cardinality of the irrationals is much larger than the cardinality of the rationals.
To be honest, you need a real analysis course to understand this, but (assuming I'm right) it's not much more than that.
Hi, one thing I don't seem to understand about Borel set. is that it says Borel set is the smallest sigma algebra set that contains all the open sets. Why smallest? How does it make a significant? What are not the smallest sigma algebra set? can you help me please.
The Billa - 2016-01-24
Bro you're huge. And good explanation.