Measure Theory 1.2 : Sigma Algebras and the Borel Sigma Algebra

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  • Опубликовано: 21 дек 2024

Комментарии • 61

  • @jeffreyhowarth7850
    @jeffreyhowarth7850 7 лет назад +14

    I studied p-adic for a month. What interested me about p-adics is people where doing things with p-adics ,like solving the zeta function, so me liking your clarity on the white board and the all the abstract material about p-adics online and having looked up the zeta function in p-adic form was looking for a enjoyable math language interpreter like yourself.Myself a math hobbies about 8 years. thanks for you math energy.

    • @Fematika
      @Fematika  7 лет назад +2

      I appreciate it!

  • @duckymomo7935
    @duckymomo7935 7 лет назад +33

    time for a measure theory joke:
    when you realize a set is not in the sigma-algebra: my set is immeasurable and my proof is ruined.

    • @Fematika
      @Fematika  7 лет назад +4

      I think this only works when you have the image along with it.

    • @michaelempeigne3519
      @michaelempeigne3519 6 лет назад +2

      lol

    • @ozzyfromspace
      @ozzyfromspace 4 года назад

      @@Fematika haha no, it was as solid joke 😂😂😂 “My set is immeasurable, and my day is ruined” 😂😂 I can’t with you people lol

  • @afzalsoomro7950
    @afzalsoomro7950 2 года назад

    Very impressive can you suggest book for measure theory for self study

    • @Fematika
      @Fematika  2 года назад +1

      I think Rudin Complex and Real analysis is pretty good. Any answer you find online will be as good as mine, this series wasn’t based on any particular text.

    • @afzalsoomro7950
      @afzalsoomro7950 2 года назад

      Thank you brother

  • @matouspikous
    @matouspikous 4 года назад +1

    I love the short format of these videos.
    Btw. Am I the only one who gets an advert every 5 minutes?

  • @Info_rare
    @Info_rare Год назад

    0:39 : the function assigns all elements of segma into R star? Shouldn’t be R+

    • @Fematika
      @Fematika  Год назад

      Includes infinity, the extended real numbers.

  • @ruthauma1141
    @ruthauma1141 5 лет назад +2

    This is impressive. Am doing my degree but it is so hard to understand this concept but you are only thirteen and you understand. Thank you for this video anyway

  • @nounoumath2467
    @nounoumath2467 7 лет назад

    8:11 we don't need X to be part of gama, all what we need is that gama is not empty since the new set is closed under complement.

  • @fvveb2141
    @fvveb2141 5 лет назад

    Your videos are really good and impressive!!!

  • @duckymomo7935
    @duckymomo7935 7 лет назад +1

    yay, your videos are exciting

  • @ΕιρηνηΘεοδωρου-θ9υ
    @ΕιρηνηΘεοδωρου-θ9υ 3 года назад

    Hi friend! I have a question! Could you please give an example of a Borel set that is neither Gδ nor Fσ;

    • @Fematika
      @Fematika  3 года назад +1

      Take the negative irrational numbers and union them with the positive rational numbers. Rationals aren't G Delta but are F sigma, that'll help you prove why.

    • @ΕιρηνηΘεοδωρου-θ9υ
      @ΕιρηνηΘεοδωρου-θ9υ 3 года назад

      @@Fematika thank you so much!

  • @deconfinedQPT
    @deconfinedQPT 6 лет назад +13

    Just wondering how do you learn?, do you study a lot?, how things make sense for you?. I am just very impressed by your capabilities at this age and it is very intriguing for me, did you get your IQ measured?. I am truly sorry if I am getting too personal I am just very interested in understanding intelligent people. Thank you for the content as well but my background is not enough to comprehend with it. I wish you could do some physics as well.

  • @willnewman9783
    @willnewman9783 5 лет назад

    Can you explain what Sigma is?
    You say it is the set of all sequences of countable unions and compliments of elements of Gamma. What is meant by sequences? A sequence is typically a function from N to your set, and would thus not be an element of P(X)

    • @Fematika
      @Fematika  5 лет назад +1

      Basically a sequence of elements of gamma, and then between the previous term and the next you do an intersection, union, or you complement the previous set and then take the intersection or union. So you’d do x_1 (operator 1) x_2 (operator 2) ... (operator n-1) x_n, where x_i is a sequence of elements of gamma, and each (operator i) is one of those operators described.

  • @arthurgames9610
    @arthurgames9610 4 года назад +10

    (Obs.: My english is really bad, so please, forgive me if I make a mistake)
    Fematika, Im a 12 years students (in august ill do 13) and I really love mathematics (as you can see, my profile pic is hilbert)! Im learning it since last year and I dont know so much about topology, metric spaces and this advanced things, but I know some calculus, set theory and other no so advanced things, and Im TRYING to learn some real analisys, linear algebra and abstract algebra via internet, and you give me a hope that some day ill actually understand category theory, algebraic topology, and this more complicated things! Keep with your work, Im sure that you are also a inspiration for a lot of students like me!

  • @Pemmykemmy
    @Pemmykemmy 7 лет назад +1

    Nice explanation. What book(s) do you like for learning measure theory?

  • @professionalprocrastinator8103
    @professionalprocrastinator8103 5 лет назад +3

    Good content. I just discovered your channel and was favourably impressed by your level of education, knowledge and intellectual maturity at such a young age. Your vids are also remarkably useful to me cause I want to learn the basics of measure theory without wasting too much time into the rigours and cumbersomeness of a uni lecture.
    Around 10:00, you start to prove that "given a certain subset of P(X), there exists a sigma-algebra that contains it" and proceed to construct such a sigma-algebra Sigma. You just assumed that it satisfies (i) but can't this be proved directly? Gamma can be considered to be a union of elements of X, so by construction, taking the union with its complement in X should just yield X. X = (Gamma) U bar(Gamma) is an element of Sigma.

    • @Fematika
      @Fematika  5 лет назад +1

      Yes, that is obviously the reason, I just forgot about it, couldn’t come up with it quickly, and didn’t have editing so I just played it safe.

  • @njchristoffersen
    @njchristoffersen 6 лет назад +2

    Don't forget at 1:15 that it is subadditive, that is to say that it is less than or equal too. Unless of course, you claim that A_i's are disjoint. Great stuff!

  • @ilka555
    @ilka555 3 года назад

    My man this is amazing! Could you please teach me stochastic calculus instead of my prof?

    • @Fematika
      @Fematika  3 года назад

      I might start making videos again soon, so maybe.

  • @2011sjw
    @2011sjw 6 лет назад

    .......once again, nicely done,......... beautifully lucid..........!!!............thanks kindly.

  • @zafdu93
    @zafdu93 5 лет назад

    nice video, my teacher mentionned how set-generated sigma algebras constructed (by definition it is the intersection of every sigma algebras that contains the set) but apparently there is another way of constructing it, by adding enough sets to your set of sets (sic)

  • @muhammadhaider7579
    @muhammadhaider7579 6 лет назад +1

    If I need to ask about Measure theory. how can i reach out you>

    • @Fematika
      @Fematika  6 лет назад

      fematikaqna@gmail.com is my new email for asking these sorts of questions!

  • @TheWitness1001
    @TheWitness1001 6 лет назад +4

    How old are you dude? These vids are amazing.

    • @Fematika
      @Fematika  6 лет назад +3

      I'm thirteen!

    • @chessislife3429
      @chessislife3429 6 лет назад +2

      Wow, thirteen years old alr study measure theory O_O

    • @EvanZamir
      @EvanZamir 6 лет назад

      Hey, this is so impressive. Can you list some of the (favorite) books you've used to learn this stuff that you would recommend for self-study?

    • @Fematika
      @Fematika  6 лет назад +5

      I did not use any books, but did use many online lectures. If you look in the comments on these videos, you'll be able to see many of the ones I use (I don't have the time right now to find and list them out).

    • @barbaramaldonado2195
      @barbaramaldonado2195 5 лет назад

      @@Fematika You explain things in a way that is very concise and easy to understand. You are literally the best!!!! KEEP DOING WHAT YOU"RE DOING

  • @johncharles3907
    @johncharles3907 4 года назад

    Can I buy a piece of your future income?

  • @michaelempeigne3519
    @michaelempeigne3519 7 лет назад

    Can you do some videos on Boolean Algebra ?

  • @muhammadhaider7579
    @muhammadhaider7579 6 лет назад +3

    You are thirteen...
    And teaching measure theory....
    Wow,
    How is this possible...!
    Tremendous effort

  • @jeffreyhowarth7850
    @jeffreyhowarth7850 7 лет назад

    Do you do p-adic numbers

    • @Fematika
      @Fematika  7 лет назад +1

      Yeah, I'll do one today.

  • @marylivesong357
    @marylivesong357 6 лет назад +1

    You are amazing man ! I am in my bachelor degree and I am learning from you .Surely you will have a brilliant future .please can I be in contact with you ,I will surely need you teacher :)

    • @Fematika
      @Fematika  6 лет назад

      My email is fematikaqna@gmail.com

  • @ElColombre27360
    @ElColombre27360 6 лет назад +1

    Jesus! How old are you?? Are you already doing this????

    • @Fematika
      @Fematika  6 лет назад +5

      Yeah, I'm doing this. You should check out some of my other videos if you really wanna be impressed! I'm fourteen now, thirteen while making this video.

    • @ElColombre27360
      @ElColombre27360 6 лет назад

      Interesting. How do you get this? A special school or something?

    • @Fematika
      @Fematika  6 лет назад +3

      I have the internet, and I go to a normal public school.

    • @ElColombre27360
      @ElColombre27360 6 лет назад

      You do it all alone? Impressive, good for you! Ad maiora! 👍💪

  • @akhiljalan11
    @akhiljalan11 6 лет назад

    4:38 I think you meant to say countable unions, not arbitrary.

  • @edwinaugustine5093
    @edwinaugustine5093 6 лет назад

    hello, im makcik bawang

  • @skyph2048
    @skyph2048 3 года назад

    sigma balls lol