This is a great video getting at core concepts of the topic. A measure theory class I had when I got my PhD was the most difficult class in all of my education. The professor was quite good and even wrote a real textbook for it, but I would have really appreciated a roadmap like this immensely. It would have helped to synthesize the learning and provide a better context of where all the pieces of the puzzle go. Thanks for making this.
Thanks for this video! I appreciate that you mentioned the power of the Lebesgue integral not just allowing us to integrate more functions but also that it gives us nice convergence theorems (fatou, MON, DOM) and other nice tools such as complete Lp spaces
This video is a really nice encapsulation of the intuitions behind the Lebesgue Theory, the animation and the commentary is very good. The channel is new and unlike other subject you won't find the buzz with math videos, but still maths videos have the advantage of being timeless so I'm ready to bet anything that on the long term the number of view on this video are going to grow arithmetically ;-) !
Can you suggest me any measure theory book that suitable for undergrad? I want to impress my class with special integral calculating techniques but almost all book I got is from Graduate level
I'm reading Sheldon Axler's "Measure, Integration and Real Analysis" which I think is amazing for an introduction (it covers lots of intuitive ideas while remaining rigorous, and presents the motivation of measure theory well). You might not get many integral techniques from any measure theory books though, since measure theory tends to be theoretical over applied.
Great video. I have a doubt. The power set is a sigma algebra. To my understanding we construct the whole idea of a sigma algebra to consider the meassurable sets, but I can already construct a meassure space from a set X and 2^X(the power set), thus including all subsets, being messsurable or not...
The problem is that we are often not able to define a measure on all subsets. For example when working with the real numbers, we want a measure with assigns to each interval the length. We can construct such a measure on a suitable sigma algebra, but it is not possible to define a measure with this property on the power set (See Vitali sets).
@ Then my question is why do we use sigma algebras in the first place? To my understanding, we justify the use of them because in principle we avoid non-measurable sets, but if the power set is itself a sigma algebra and it contains non measurable sets, then...
I get it’s faster to throw a GPT generated, corrected script against a TTS and have some manim code do the rest but it makes it hard to follow and trust the contents… won’t fuck with this. Thanks for the effort nonetheless, human.
This is literally everything I learned in probability theory last semester lol. Thanks for the nice and high-quality video!
This is a great video getting at core concepts of the topic. A measure theory class I had when I got my PhD was the most difficult class in all of my education. The professor was quite good and even wrote a real textbook for it, but I would have really appreciated a roadmap like this immensely. It would have helped to synthesize the learning and provide a better context of where all the pieces of the puzzle go. Thanks for making this.
Thanks for this video!
I appreciate that you mentioned the power of the Lebesgue integral not just allowing us to integrate more functions but also that it gives us nice convergence theorems (fatou, MON, DOM) and other nice tools such as complete Lp spaces
This video is a really nice encapsulation of the intuitions behind the Lebesgue Theory, the animation and the commentary is very good. The channel is new and unlike other subject you won't find the buzz with math videos, but still maths videos have the advantage of being timeless so I'm ready to bet anything that on the long term the number of view on this video are going to grow arithmetically ;-) !
The quality of logic is overwhelm ing😊😊😊
Your voice sounds AI-generated and the unusual and incorrect intonations make it difficult to follow along with the content.
yeah i’m not messing with this because of the AI-generation. bummer.
It sounds like AI because it is AI
yeah pass
Really good video. Thank you so much!
NIce channel! All the best!
Thanks a lot!
This is awesome! Showed up on my feed just as I needed to learn it for class lol
Glad it was helpful!
Excellent video ❤
Great video!
Very nice. Subscribed and I will be watching all of your videos in the coming weeks.
Nice video...I see this channel is new. I wish you the best of luck and keep uploading!
Can you suggest me any measure theory book that suitable for undergrad? I want to impress my class with special integral calculating techniques but almost all book I got is from Graduate level
I am not sure whether it is suitable for undergrades, but i found Roydens Real Analysis very helpful.
Heinz Bauer, measure and integration theory
Tao's Analysis II and Pugh's Real Mathematical Analysis are aimed at undergrads and each ends with chapters on Lebesgue theory
I'm reading Sheldon Axler's "Measure, Integration and Real Analysis" which I think is amazing for an introduction (it covers lots of intuitive ideas while remaining rigorous, and presents the motivation of measure theory well). You might not get many integral techniques from any measure theory books though, since measure theory tends to be theoretical over applied.
@@muhammadmahdidacosta5188 Do i have to master the metric space concept before measure theory? It seem require knowledge topology of real number
I didn't understand anything because it was just a resume of things...
Great video. I have a doubt. The power set is a sigma algebra. To my understanding we construct the whole idea of a sigma algebra to consider the meassurable sets, but I can already construct a meassure space from a set X and 2^X(the power set), thus including all subsets, being messsurable or not...
The problem is that we are often not able to define a measure on all subsets. For example when working with the real numbers, we want a measure with assigns to each interval the length. We can construct such a measure on a suitable sigma algebra, but it is not possible to define a measure with this property on the power set (See Vitali sets).
@ Then my question is why do we use sigma algebras in the first place? To my understanding, we justify the use of them because in principle we avoid non-measurable sets, but if the power set is itself a sigma algebra and it contains non measurable sets, then...
Great !
I get it’s faster to throw a GPT generated, corrected script against a TTS and have some manim code do the rest but it makes it hard to follow and trust the contents… won’t fuck with this. Thanks for the effort nonetheless, human.