FTiP/2. Limsup of events

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  • Опубліковано 22 січ 2025

КОМЕНТАРІ • 13

  • @sarahk6965
    @sarahk6965 4 роки тому +3

    this video was so helpful! better than any of 10 previous videos i watched!

  • @islamatef2526
    @islamatef2526 Рік тому

    I have a question
    Ingeneral
    Can I say that the union of A sub n is the supremum of all An ?
    And the intersection of A sub n is the infimum of An ?

    • @martonbalazsuob4363
      @martonbalazsuob4363  Рік тому

      It sounds logical to me but I haven't actually come across supremum or infimum of events before.

  • @texla-kh9qx
    @texla-kh9qx Рік тому

    Questions:
    1. What if for all n, it is always a fixed event A_K occurring? as it is true for all n, K could be only infinity. Is this scenario not making sense? but if it is possible then it's not infinitely many of A_k occur?
    2. Do we need to impose an order on A_k here? from MT/2 Continuity of measure, the concept of limit on events exists only for increasing or decreasing A_k's. I am trying to understand the connection of limsup of events to limsup of functions. Here, the union piece looks like finding a sup (if increasing) from MT2 and then the intersection piece looks like taking a limit (if decreasing).

    • @martonbalazsuob4363
      @martonbalazsuob4363  Рік тому +1

      1. I think you are over-complicating this. We have events A_1, A_2, A_3, ... each of which may or may not occur. What is the question?
      2. Indeed there is the natural order in the indices: A_1, A_2, A_3, ... There is no order required on the sets themselves; they do not need to be increasing or decreasing. You are right that the union (on events) has a flavour of sup (on functions): the union occurs iff at least one of the events occur. Now, this union from n...infty will be decreasing as a function of n (the more n, the less sets in the union, so it can only decrease), this might be the ordering you are missing. Hence the intersection in front is actually a set-limit even if the A's themselves are not ordered.

  • @dinushimadushika2081
    @dinushimadushika2081 3 роки тому

    Why its not visible

  • @sarahk6965
    @sarahk6965 4 роки тому +1

    can you please make a video for liminf of events?

    • @martonbalazsuob4363
      @martonbalazsuob4363  4 роки тому +2

      I'm not using that in this unit, so I have no plans to make a video on it. The Wiki page en.wikipedia.org/wiki/Set-theoretic_limit seems to do a good job explaining these.

  • @edwardhartz1029
    @edwardhartz1029 3 роки тому +1

    This video has really helped, thanks so much.

  • @rabiasagheer1426
    @rabiasagheer1426 3 роки тому

    That is the most simplest explaination thank you .

  • @uberwachGG
    @uberwachGG Рік тому

    Our handwritten script looks almost the same 😁