Measure Theory 1 | Sigma Algebras

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Watch the whole video series about Measure Theory and download PDF versions and quizzes: tbsom.de/s/mt
There is also a dark mode version of this video: • Measure Theory 1 | Sig...
There is also a bright mode version of this video: • Measure Theory 1 | Sig...
To find the RU-vid-Playlist, click here for the bright version: • Measure Theory
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And a big thank you for everyone who contributes to the subtitles here: github.com/thebrightsideofmat...
This is my video series about Measure Theory. I hope that it will help everyone who wants to learn about it. We discuss sigma algebra, measures, and integration. For any questions, please leave a comment or come to the community forum of the Bright Side of Mathematics: tbsom.de/s/community
#MeasureTheory
#Analysis
#Integral
#Calculus
#Measures
#Mathematics
#Probability
This is part 1 of 22 videos.
00:00 Introduction
00:58 Measuring lengths
03:00 Example power set
03:51 Definition sigma-algebra
10:20 Example for sigma-algebras
(This explanation fits to lectures for students in their first year of study: Mathematics for physicists, Mathematics for the natural science, Mathematics for engineers and so on)
The Bright Side of Mathematics has whole video courses about different topics and you can find them here tbsom.de/s/start

Опубликовано:

26 июл 2024

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Комментарии : 344

@brightsideofmaths 3 года назад

Please do the quiz to check if you have understood the topic in this video: thebrightsideofmathematics.com/measure_theory/overview/ There is also a dark version of this video! ru-vid.com/video/%D0%B2%D0%B8%D0%B4%D0%B5%D0%BE-xZ69KEg7ccU.html

@NilodeRoock 2 года назад

"Page not found" ?

@brightsideofmaths 2 года назад

@@NilodeRoock I've updated the link now :)

@NilodeRoock 2 года назад

@@brightsideofmaths Thank you.

@suhaibalkhaldi Год назад

Thank you very much sir

@lehoangsonsg7436 4 года назад

What you are doing is amazing. I hope you can produce more content in English for non-German speakers.

@Gaeisok Год назад

I honestly feel like learning German to get access to mroe videos

@roger9822 4 года назад

Amazing mini-course series, it helps a lot to get through probability theory. Although your videos are short and illustrative, you never lose mathematical rigidity. Thank you so much!

@Artonox 4 года назад

THANK YOU GOD FOR BRINGING YOU INTO THIS WORLD. I finally found someone who can actually teach measure theory online! Ive always had this on my mind (my worst subject in mathematics, because i didnt understand my lecturer), and finally, nearly 8 years later, you made this beautiful video series for me to revisit and you explain very well. I did get a first class in the end, but I really was interested in measure theory and ashamed that i wasn't able to do this well. This serves as a second chance for me!

@NilodeRoock 2 года назад

Say things like "THANK YOU GOD FOR BRINGING YOU INTO THIS WORLD." to your parents, spouse or siblings, if you have to. Go and support the content provider financially if you want to say thanks. Just my 0,01c.

@zhaoyuzhu254 3 года назад

I literately spent 12 mins on RU-vid and understand the whole thing, while I spent 2 hours on my professor's recording and still have no idea what he is talking about. :)

@brightsideofmaths 3 года назад

Thanks :)

@scarlettliu885 2 года назад

I have the same experience as yours.

@nreceda 3 года назад

Just found your channel. I am taking a course this semester on Stochastic Processes and as far as I can tell, your explanations are much easier to understand so thank you thank you thank you thank you.

@mercymuenimwangi9064 3 года назад

It reached a point I just had to search measure theory for dummies. This is the best tutorial. I immediately subscribed and turned on notifications. Thank you so much

@thedan2 4 года назад

Amazing video! Amazing series! Please keep it coming! Measure theory has never been easier to understand. Thank you!!

@afrolichesmain777 4 года назад

Wow great explanation for an introduction to sigma algebra. It’s my first time looking at this material. Looking forward to the rest of your videos on Measure theory!

@julianvillaquira4127 5 лет назад

Your channel is amazing! Thanks for the videos, they are very helpful to me since I will take a measure theory course next semester. New subscriber 😀.

@Thaizir 3 года назад

Thanks for taking the time to produce this content, it brought me back memories when I was studying this course.

@igorkuivjogifernandes3012 Год назад

This is a nice video! I took measure theory in undergrad and I loved the subject, although it was so abstract. Your videos definetely will help this make make sense to many people!

@brittnihall1688 4 года назад

These videos are amazing and incredibly helpful!! Thank you SO much!!

@giorgiozannini5626 5 лет назад

Thanks man you saved me! Studying Bayesian statistics now and couldn't wrap my head around the whole measure stuff. Thank you very much again!

@RenyxGhoul 2 года назад

Even more succinct and concise than my lectures but I understand it a lot more. Wow. Thank you!

@axelperezmachado5008 4 года назад

This channel is amazing! So glad i found it! I subscribed of course

@rmbennet 2 года назад

I came here a year and a half ago I couldn’t understand any of it after the first one or two videos. it’s remarkably more intuitive after abstract algebra and real analysis. It’s actually really interesting.

@sejuprajapati2005 4 года назад

Thank you so much for all videos. Your teaching skill is amazing.

@lieignatius9009 4 года назад

This video helped me a lot, thank you!

@daviddavini847 2 года назад

This was incredibly helpful, thanks for the knowledge!

@davidwright8432 4 года назад

Thanks; amazingly clear! I hope I'll be able to follow as easily when after a bit more development, you actually start do things with the ideas!

@cardinalityofaset4992 Год назад

Just a minor technical detail: You can slightly generalize the definition of sigma algebra by excluding the empty set from the first condition. Its presence in the sigma algebra immidiately follows from the fact that X must be measurable and that any complement of a measurable set is also measurable. (X^c = X \ X = 0 => 0 is measurable). Awesome list of vidoes, it´s intuitive and entertaining to watch :)

@johnnyq4260 8 месяцев назад

I bet when he wrote that he was thinking about topology.

@gulshanamna3796 Год назад

You are the one who really can make students as well as teachers to understand measure theory in real meanings

@brightsideofmaths Год назад

Thank you very much :)

@gustafa2170 3 года назад

I'll come back to this video when I'm stronger. Need more training.

@brightsideofmaths 3 года назад

Just farm some EXP on my lower level videos ;)

@danialdunson 2 года назад

buy more pots

@nathanbarnard7896 3 года назад

Just starting measure-therotic probability theory and these are great :)

@pk_1320 4 года назад

Loved it, great video!

@shreykabir 2 года назад

Thanks a lot... I was interested in measure theory and wanted to learn more about it... This video has helped a lot making it easier for a high school to understand...

@perkelele 3 года назад

Summary: A measure is a map of the generalized volume of the subsets of X. Power-set: set of all subsets of a set X. if X = {a,b} then P(X)={empty,X, {a}.{b}} Measurable Sets: We don't need to measure all the subsets we can form, only some of them. Can be the whole power-set, but is useful smaller. Useful because generalizing length in a meaningful way doesn't work for all sets, but only some sets. A is a Sigma Algebra: each element is a measurable set a) Empty set, and Full set are elements of A b) If a subset is measurable then so is its complement c) If every individual countable set is part of the sigma algebra, then the union of all these sets is also in the sigma Algebra To speak of an area of A we need for the sets that make it up to be measurable. So if you take all the individual sets (units) that make it up, you will get the whole. The smallest sigma algebra A = {emptyset, X} it validates all three rules. The largest sigma algebra A = P(X) because it contains all the subsets. In the best case scenario we can measure them all. But this is not the case so we are often between these two cases.

@marekbalcerzak5255 2 года назад

I love to watch your videos to get notion about the subject before reading handbook. Great job !

@brightsideofmaths 2 года назад

Thanks :)

@harshavajpayee7652 4 года назад

Now after watching this I can say that measure theory is measurable 😅 Thanks for this wonderful video ❤️

@jiahao2709 3 года назад

You are the professor of MIT level, you video lectures should be accepted, respected, appreciated and advocated!!!!!!!!

@evionlast 4 года назад

Clearly explained, basic examples, very good

@monsijbiswal1104 3 года назад

Just awesome. Loved it!

@yujinlee8188 3 года назад

This is amazing!! Thank you so much 🙏

@jasonlim8387 2 года назад

Thank you, it was a very helpful video!

@pointofview6679 3 года назад

Thanks so much sir.This is amazing and helpful

@tropicalpajamas9986 4 года назад

Very well explained with straightforward and intuitive examples. We neeeeeeeeed more of this exciting course in Mathematics. Keep it up~!!!

@PostModernAlchemist 2 месяца назад

I have no idea how youre making this subject so approachable for someone who took real analysis and abstract algebra 10+ years ago, but thank you! This is great!

@brightsideofmaths 2 месяца назад

Wow, thank you! :)

@RAJ6118 2 года назад

Beautiful insight of the topic

@rgoswami 4 года назад

Fantastic work!

@xPlosiveFobx 3 года назад

Thank you this helped so much!

@wesolyfoton 2 года назад

Great explanation. Kudos!

@arefpourseyedi8087 Год назад

The presentation was amazing. Thank you!

@brightsideofmaths Год назад

Glad you liked it!

@sebon11 3 года назад

Great video, man!

@DimiqBaba 3 месяца назад

Thank you, straight after the lecture I watch your lectures.

@brightsideofmaths 3 месяца назад

Best idea :)

@syamalchattopadhyay2893 3 года назад

Excellent video lecture

@jatayubaxi4553 4 года назад

Absolutely clear explanation.

@STgauss3268 2 года назад

The moment I realised this dude is giving a brief explanation on Measure Theory, I subscribed immediately.

@sallanmega1 2 года назад

This is actually a great explanation. Greetings from Spain!

@mobilekaki8402 5 лет назад

Thank you so much. now finally i can understand it.

@rivology8423 2 года назад

Love you’re videos

@andreaorsi2015 4 года назад

good job mate thanks a lot, subscribed

@psytno 4 года назад

thank you really I enjoy these topics

@lyubomir.andreev 4 года назад

Great video!

@richardgreenhough Год назад

Tried to understand this from a book and didn't. This video enabled me to grasp this easily. Great video!

@brightsideofmaths Год назад

Glad it was helpful!

@TDRT23 10 месяцев назад

THIS VIDEO IS AMAZING!!

@jotajota278 3 года назад

Extremely clear and nice. Thank you so much! New subscriber here.

@idontthinkso5966 Год назад

My goodness, you really do have a video in everything I'm looking for.

@brightsideofmaths Год назад

Thank you very much :)

@rafaelb.333 4 года назад

So glad I've found your channel. Which book did you use to study this?

@IhrffhhgJgfhhbvf Месяц назад

I finally understand why a sigma algebra is the way it is. The drawing made it so clear to me

@brightsideofmaths Месяц назад

Nice :)

@babumaths8066 Год назад

Very useful. Thank you sir.

@garrycotton7094 4 года назад

Great video :D. This reminds me of Group Theory in a way. Empty set, A in Fancy A is like the identity axiom. Complement of A in Fancy A is like the inverse axiom. Union of A_i in Fancy A is like the closure axiom.

@axelperezmachado5008 4 года назад

does this mean that a sigma-algebra is a group under union?

@deept3215 4 года назад

@@axelperezmachado5008 It isn't because there is no inverse of union in the sigma algebra

@axelperezmachado5008 4 года назад

@@deept3215 True! Haven't realised

@Sciophile 4 года назад

@@axelperezmachado5008 It's an abelian group with respect to the operation of symmetric difference.

@mikiti6870 9 месяцев назад

Thank you, really great work :)

@brightsideofmaths 8 месяцев назад

Glad you liked it!

@tunafish1274 4 года назад

Nice video!

@pedromazariegos6536 9 месяцев назад

I love your work man

@brightsideofmaths 9 месяцев назад

Glad you enjoy it! And thanks for your support :)

@ramkumarr1725 3 года назад

Very nicely explained. And truly innovative to link it up to the quiz. I will try to see the other videos but the first chapter was very good.

@brightsideofmaths 3 года назад

Thank you! I also want to do quizzes for the other parts if they are helpful.

@ramkumarr1725 3 года назад

@@brightsideofmaths They are helpful for retention of material and application, IMHO. Math is not a spectator sport, IMHO.

@josmithephraim9078 4 года назад

Wow!! These explanations are really nice. Immediately subscribed 👌

@josmithephraim9078 4 года назад

What books can we refer to understand more about Measure theory, distribution functions, chebyshev lemme etc?

@brightsideofmaths 4 года назад

There are a lot of books. I really like Schilling's about measures and other stuff :)

@josmithephraim9078 4 года назад

@@brightsideofmaths Danke gut !

@user-ib4bg9kg5s 3 года назад

The name is so scary, so we need people like you in this world to make them look less intimidating, thanks for the explanation

@shraddha5588 2 года назад

Thank you ! its such a good explanation.

@brightsideofmaths 2 года назад

Glad it was helpful!

@user-lx4wr8rt4s 3 года назад

My man, you kinda sound like Mimir from God of War. Loving it!

@ssmhsasd 9 месяцев назад

Very intuitive explanation, thank you. Very helpful for Engineers 👍

@brightsideofmaths 9 месяцев назад

Glad it was helpful! :) And thanks for the support!

@lexluthor6975 4 года назад

Very insightful explanations. Some people are born lucky!

@Wynell 8 месяцев назад

Thank you so much here! I have an exam in a few days and you're literally saving me :)

@brightsideofmaths 8 месяцев назад

Happy to help! :) And thanks for the support!

@YitzharVered 3 года назад

I went through this crap in introduction to probability and was totally lost. Thank you for explaining.

@Cowux 2 года назад

Best measure theory video on YT!!!!

@brightsideofmaths 2 года назад

Glad it was helpful!

@bilalghermoul3634 3 года назад

Many thanks for these good and helpful mini-lectures. And I would like you to direct me to a useful textbook on this theory from your point of view.

@mohamedamin491 2 года назад

Thank you very much.

@JuanRodriguez-tr6st 3 года назад

You are one of the best teachers I’ve had

@JuanRodriguez-tr6st 3 года назад

Came here for functional analysis, stayed for measure theory

@_Navani_ 4 года назад

This is such a helpful video! Now i feel like i can pass measure theory

@boyzrulethawld1 4 года назад

What course are u taking this for? 🤔

@cvdvdfhgh4946 3 года назад

@@boyzrulethawld1 id guess measure theory

@td_27 Год назад

Beni buraya kadar getiren eğitim sistemimize teşekkür ediyorum.

@lishenhe3801 2 года назад

Awesome videos

@hamzehabuabed6333 3 года назад

Thanks so much

@kkkk-oy9qv 4 года назад

Thank you, you are the best

@Zubair622 3 месяца назад

Extremely marvelous explanation really enjoyed it Please also upload lectures of complex analysis

@brightsideofmaths 3 месяца назад

Already done. See here: tbsom.de/s/ca

@Zubair622 3 месяца назад

Thanks sir

@lidiias5976 Год назад

Thank you!

@armatg 3 года назад

This is the first video where i understand what a sigma algebra is, thank you!

@varnita4455 2 года назад

Thank you.

@ker0666 11 месяцев назад

Great ! Thank you.

@Raibows1226 8 месяцев назад

Thank you 🙏🙏🙏🙏 I finally understood

@brightsideofmaths 8 месяцев назад

You are very welcome :)

@time_traveller24 3 года назад

helpful video

@abdulghanialmasri5550 2 года назад

Man, you are a great teacher 👍

@brightsideofmaths 2 года назад

I appreciate that! Thanks :)

@JJ-fb2lp 4 года назад

Jesus dude. I have not seen any one that can explain this topic better than you, which can mean two things. 1. They don't understand the topic 100% but is trying to teach someone. 2. They don't know how much to dumb it down for people who are just trying to understand this topic.

@NewCalculus 4 года назад

You've never understood it because nonsense cannot be understood, only believed.

@MrOvipare 3 года назад

I was reading Cybernetics : or control and communication in the animal and the machine by Norbert Wiener yesterday... I was surprised by the fact that I got totally lost when he used concepts of "measures" in the chapter about groups and statistical mechanics. What game is this!? What are those objects? Turns out I didn't knew shit about measure theory, despite my physics and engineering studies + working in R&D. This is exactly where I needed to land!

@Anteater23 3 года назад

Would you ever consider making a maths series on the subject of topology? Your videos are brilliant!

@brightsideofmaths 3 года назад

Thanks! I want to do that, yes :)

@Anteater23 3 года назад

The Bright Side Of Mathematics :) topological spaces just seem harder to visualise than metric spaces for me. Metric spaces felt like a very natural concept.

@brightsideofmaths 3 года назад

@@Anteater23 Topological spaces are also very natural. Often the concrete distances between points are not import but just the knowing which one is near or far.

@chanderlerbing6347 2 года назад

Hi, thank you so much for posting this series! It helps me a lot with my analysis course! Also I have a question here: since the power set of a set X is always sigma-algebra, does that mean any subset which belongs to the power set is measurable with regard to the power set?

@brightsideofmaths 2 года назад

Thank you very much for the question! You are completely correct :)

@uzivatel123 Год назад

thank you

@mushroomsteve 4 года назад

Proposition: A sigma-algebra F is closed under finite intersections. Proof: Let F be a sigma algebra on a set X, and let A and B be elements of F. Then (A n B) = ((A^C u B^C)^C). Therefore, (A n B) is an element of F. Corollary: A sigma-algebra that is closed under arbitrary unions is a topology.

@sheerrmaan 4 года назад

Because the complements of A and B must belong to the sigma algebra by condition II. And the union of these two complements also belongs by III. And again the complement of it belong to F.

@mushroomsteve 4 года назад

@@sheerrmaan Exactly.

@DeadPool-jt1ci 4 года назад

what kinda of maths are prerequisites for this ? i'd say i'm fairly decent in calc 1,2,3 / differential equations / linear algebra / prob /stats ,and i ve also completed a real analysis course (first 7 chapters of rudin's principles of mathematical analysis)