The best explanation of Sigma Algebra I have found on KZitem. Thank you kindly. I finally understand now.
@kevin_m_smith
7 жыл бұрын
Great description and examples! This cleared things up for me
@marcoosyo6222
4 жыл бұрын
U are the best!!!!!!!!!!!! Even in my native language I cound´t find someone with this great and clear explanation.
@Gengar99
3 жыл бұрын
I watched 2-3 sigma-algebra before this and this video had the better explanation for me, thank you.
@vrushalibhise7375
3 жыл бұрын
I just realized that my college professor used the exact same notes for explaining Sigma algebra! thankyou
@kushalneo
3 жыл бұрын
Nice informative video. As per my understanding, at 6:40, Omega={1,2,3} and {Omega}={{1,2,3}} are two different thing. {Omega} is a member of T not the Omega. Kindly correct me if I am wrong.
@clemz26
6 жыл бұрын
Thanks for the video. It is clear, and answered all my questions :D
@kirandeshmukh8725
3 жыл бұрын
This leacture is really awesome
@user-qr9dk3gz5k
4 жыл бұрын
Thank you for you video! You've made it very easy to understand.
@zildijannorbs5889
2 жыл бұрын
Besides the notation thing, great material! Really makes me wanna rip through my probability problems lol.
@tomtian895
4 жыл бұрын
Hey ya, I find your video very clear and comprehensive. Can you provide a sequence of watching? Also can you make more videos like these. Thank you!
@tavrion
12 жыл бұрын
Thank you for taking the time to make this.
@dalegillman5287
3 жыл бұрын
Thanks, great video, friend.
@jingwan49
10 жыл бұрын
Awesome. Easy to understand.
@thybowllingman2752
6 жыл бұрын
thanks, that was actually pretty helpful. Keep it up!
@mairamunir8344
9 жыл бұрын
Helped me with my homework. Thanks
@freddy4960
9 жыл бұрын
Thank you very much! Very good explanation!
@crazychic1990
10 жыл бұрын
you deserve heaven sir
@Matematica_Aplicada
7 жыл бұрын
Very clear! Thanks!
@everyonesmeow
11 жыл бұрын
thanks for clear explanation.
@Zanoula06
10 жыл бұрын
Thanks, very very helpful!!!!
@minato232
4 жыл бұрын
Thanks good i finally find an example about what isn't a sigma-álgebra, thanks man.
@SamirPatnaik
2 жыл бұрын
Very helpful. Thank you so much
@rodolfohernandez458
3 жыл бұрын
Thank you. The video is fantastic.
@wf060
12 жыл бұрын
thank you sir, you are far better than my teacher, Danke
@yousify
9 жыл бұрын
thank you so much, I noticed that you put "phi" inside curly brackets "{ }"; in set theory it states that curly brackets "{ }" is equivalent to "phi";
@motherfatherish
13 жыл бұрын
thank u so much it made me understand this topic....
@sunfender2276
11 жыл бұрын
thank you so much! I have paid for books which do not explain half as clear as you did, with the examples and all. I also thank scadqwqw for additional clarification.
@alvtal1
10 жыл бұрын
Muy bueno!! Very good
@jessievanbreda5119
6 жыл бұрын
This is great please make more videos on probability measure!
@siminliu5281
3 жыл бұрын
really really helpful, thanks!
@ranadanish4245
6 жыл бұрын
you do very nice, make more video on measure theory
@pprokics
10 жыл бұрын
Simple and very clear explanation od sigma algebra.
@bachirdh
12 жыл бұрын
Very clear video, thanks a lot ;-)
@scadqwqw
11 жыл бұрын
At about 6:15, you define the trivial set as T = { {Ø}, {Ω} }, but I think you mean T = {Ø, Ω}, without the extraneous braces. Ø denotes the empty set, and {Ø} is a set with one element (which is the empty set), so they are different. For T to be a sigma-algebra, Ø and Ω themselves must be elements of T.
@lunchguo
12 жыл бұрын
really helpful~
@deathmetal124
8 жыл бұрын
Thank you!
@PoppyPin
9 жыл бұрын
Thankyou thankyou thankyou!!
@Nathsnirlgrdgg
7 жыл бұрын
your first condition should be that omega is an element of sigma, not a subset. {omega} != omega, {omega} = {{1,2,3}}. There shouldn't be brackets around omega inside the examples. {null_set} != null_set. There shouldn't be brackets around the null_set in the examples.
@yaminnew2953
6 жыл бұрын
Nathaniel Gregg exactly
@kushalneo
3 жыл бұрын
I observed the same
@02vLxcZF
9 жыл бұрын
Thanks, very clear. Why not build on this video and explain Measure Theory?
@juanlynching3807
5 ай бұрын
its similar to properties of discrete probability distribution.p(X)=1 and 0
@RahulaSamaranayake
2 жыл бұрын
well explained
@nathaliem3322
6 жыл бұрын
THANK YOU!!
@rhlvora
12 жыл бұрын
wonderful
@delnomad
10 жыл бұрын
Dzięki !!!
@andrytino
5 жыл бұрын
There is a mistake in the notation I think. When you want to indicate that, in your first example, T = {emptyset, omegaset}, you should write emptyset without parentheses, otherwise {emptyset} and {omega} mean a set containing another set... Also, the first condition at the beginning, you should not use operator "contains" but operator "in".
@MaMeawwwwwwww
4 жыл бұрын
Totally agree with u
@luylasnubes2974
Жыл бұрын
I have a question about the examples: Why is the sample set inside brackets {Ω}? shouldn't have to be without brackets like Ω ? because we already know that represents {1,2,3} so if that is inside brackets we get: {{1,2,3}} which is not at the level of the other subsets of the collection of each example, precluding to be measurable. I talking that instead of Z = {{{}},{Ω}} we should write Z = {{},Ω} and instead of Z = {{{}},{Ω},{1,2}, {3}, {2,3}} we should write : Z = {{},Ω,{1,2}, {3}, {2,3}}
@haggaisimon7748
3 жыл бұрын
A nice and a short video. 0:49 the sign of inclusion is inaccurate. Sigma belongs to F as an element, but not as a subset.
@zenpower1684
9 жыл бұрын
There seems to be something wrong with property 1. Omega is an element of F rather than a subset of F.
@Kuxe
7 жыл бұрын
This is true. He says that Omega is a member of F, which is correct, but he have used the wrong symbol.
@luylasnubes2974
Жыл бұрын
I have another question, in the first property of the sigma-field it says that Ω ⊂ F. But as I understand the containment symbol (⊂) is used for subsets, but in this context Ω is not refered to a subset but an element of F, so shouldn't be written as Ω ∈ F the first property? Also in the second property It has A ∈ F which I consider it is correct.
@GiuseppeVittucci
13 жыл бұрын
Thanks a lot. Very clear. ;-)
@Vewyt
13 жыл бұрын
Thanks, I've got it
@gidssforever
10 жыл бұрын
Great, but at 12:53 you should add that is the cardinal of any sigma-algebra that lies between the cardinals of the trivial and power set instead of use "
@arxdeath773
8 жыл бұрын
Thanks!
@avarussurava9488
7 жыл бұрын
THANK YOUU
@Ghruul
9 жыл бұрын
when you say "F is closed under countable unions", you shouldnt just mention the finite Union, but also the countable infite union of a series Ai, where it then would say "If A1,A2,A3,...Ai,... is an element of F, then so is the union UAi from i=1 to infinity"
@VahidOnTheMove
5 жыл бұрын
As far as I understood, because of condition 1, it is not necessary to say infinite set. All you need is to change A1,A2, ... to A1 union (A1)^c (complement of A1). By this you can change infinite union to finite union. Indeed, you will have a finite union of sets.
@salim444
4 жыл бұрын
@@VahidOnTheMove It might be late but I would like to give my thoughts. suppose omega is [0,2]. and the building sets for F are of the form [0,1-1/n] and let's include their complements and all the finite unions. the set [0,1) is not in F but is in the union on all the sets we started with. F does contain omega simply because it contains the sets and their compliments,it does obey the closure under compliments and finite union by definition. F doesn't have [0,1) because if you think about the group from topology thin this is an open set in the induced topology from R onto omega but doesn't include any set of the compliments of the sets [0,1/n]. so it isn't an open set in the topology from F
@dacianbonta2840
5 ай бұрын
Are uncountable sigma algebras of computational interest, given they run smack dab into AoC+CH buzz saw?
@RafaelGonzalezDeGouveia
11 жыл бұрын
Not totally sure, but think that empty set and Omega may not be in bracket, because they are allredy a set, so is like put a set into a set
@ShailenSobhee
12 жыл бұрын
How about the the Borel sigma field?
@stepbil
13 жыл бұрын
Danke;-)
@HenriqueBSena
8 жыл бұрын
this exemples works, because you uses a finity set.
@firdovsihasanzada
4 жыл бұрын
Thanks
@HenriqueBSena
8 жыл бұрын
wrong, sigma algrebra uses infinity union. a finity union define only a algebra.
@pedroduarte6672
7 жыл бұрын
I guess you are right. if F is theta-field and if A belongs to F than the infinity union of An belongs to F.
@RafaelGonzalezDeGouveia
11 жыл бұрын
think the same
@kevinchen2167
9 жыл бұрын
I'm lost in this example; T = { {Ø}, {Ω} }, why ØUΩ=Ω and ØnΩ=Ø?
@nobodycares9797
8 жыл бұрын
+Kevin Chen You can think of the operation union as "all the elements that belong to both A and B". Likewise, you can define the intersection as "all the elements unique to both A and B". So when you have Omega U 0, you are essentially asking "if I combine all the elements of the set and the empty set, what will I get". Obviously, you get the elements of the set because the null set contains nothing. Similarly, when asking "Omega intesect 0", you are looking for all the elements you can find in both Omega and the empty set. Well, Omega has elements, but the empty set has nothing. Therefore, they have no common element, nothing between them. So the result is the empty set.
@derekchan3633
9 жыл бұрын
is {empty set} = empty set ?
@Nathsnirlgrdgg
7 жыл бұрын
Absolutely not
@yaminnew2953
6 жыл бұрын
No. He made a mistake in the video
@LaureanoLuna
12 жыл бұрын
Mind the notation of the first condition: you use the symbol of subset-of instead of the symbol of member-of. Also the definition you give later on corresponds to 'finite union', not to 'countable union'.
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