Sigma Algebras and Algebras of Sets

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***CORRECTION/FORGOT TO MENTION: in the definition of a sigma-algebra, the collection of subsets of omega, A-naught, must be non-empty to be a sigma-algebra.***

In this video:
Definition of an algebra (of sets)
Definition of a sigma-algebra
Counter-example to show that not every algebra is a sigma-algebra!
Proof that any collection of subsets of omega that is closed under complementation and finite union is an algebra.
Proof that any sigma-algebra is closed under countably-infinite intersections.

Visual math is awesome.
What other proofs would you guys like to see visualized?

[rickkix]

I found the visual explanations helpful

[sushilgupta]

I didn't understand anything but it feels me good to watching

[SliversRebuilt]

I don't know where you've gone, mysterious mistress of manatees and measure-theoretic mathematics...but I'm glad you were here! Youtube can be such a wonderfully idiosyncratic window into so many incredible peoples' lives, at times. It's quite sublime.

In all seriousness, thanks for the lovely and lucid explanation of a subtle subject! I hope you're doing well, wherever you are; and that perhaps you'll come back and teach us more measure theory some day haha

[KhanRigol]

Wow that's ma'am I love your greetings from India 🇮🇳🇮🇳

[sushantsuman]

i am student @ IIITG, you hve good way of teaching style with expression from hand, you look very beautifull its greeting from india

[abdulwaheedyarik]

Ma'am why we need measure theory and what is measure

[jayjayf]

It would be good rather than to regurgitate the definition, if you show some intuition that would be good

[pawan.p.pvideos]

Can I get a proof of two independent event s

[HaleyoBourke]

Have a question about sigma algebras? Request a proof below!

[GreenMeansGOF]

Why do measures require sigma algebras?

[normansabin]

'D' did not become a non-σ-algebra until AFTER you considered the series An, but considering the series, made 'D' in an infinite domain, specifically the natural numbers domain, which is in fact "countably-infinite" along with a countably infinite union. So why is it now defined as non-σ-algebra?

[winstonherolim]

I can't focus 🥺 Do you have facebook or Instagram?