The Mathematician's Measure

[@jaopredoramires]

Incredible introduction to Measure Theory! Giving out examples does wonders for the understanding of the theory. Can't wait to have more quick explainers on this topic. Also, why is it called "sigma" and "algebra"? Is the name arbitrary or is there some historical background?

[@enricobianchi4499]

You should make a followup where you explain how this helps us solve the problem with the cube!

[@harriehausenman8623]

Fantastic video! Thanks again for the positively-biased visuals (black-on-white) 🤗

[@AbideByReason]

Thanks. Glad you enjoyed it!

[@KashTheStampede]

Edit: Sorry, I missed the word 'disjoint'. My bad. Good explanation! It does not seem to me that the Dirac measure is a measure on the power set of X. One of the properties that you give for a measure is that the measure of the union of a collection of subsets is the sum of the measures of the sets. Consider the set X = {1,2,3}, and the Dirac measure where the fixed x=1. Now the measure of {1,2} is 1 and the measure of {1,3} is 1. Their union is {1,2,3}, which should be measure 2 by the above property, but is actually 1 by the definition of the Dirac measure.

[@QVark-d1o]

Can you continue the series to get to lebesgue integrals and proofs of dominated convergence theorem? Would be sick with manim

[@QVark-d1o]

Great explanation

[@harriehausenman8623]

Couldn't agree more

[@mukinga]

GREAAAT VIDEO KEEP IT UP

[@TheOneMaddin]

I see you are still learning. But keep it up. The quality is quite high in this video.

[@VholyIQ]

I don't see the connection of any of the algebra with the cube you show at the beginning

[@JonSebastianF]

Yeah, I have to agree. I kinda don't understand where we started, where we ended, and why we where going there? ':-|

[@williamgardner1762]

each v sub n is the volume of a smaller cube in the larger cube. Together adding up to the volume of the bigger cube

[@icosagram]

​@@JonSebastianFhe literally said in plain English that you're adding up the volumes of small cubes that combine to form a bigger cube, it's a simple concept

[@icosagram]

if you understand how addition works you should have no trouble understanding the beginning of the video

[@srghma]

@icosagram and why we need measure?

[@HesitantCicada]

Is this still manim? Looks good

[@AbideByReason]

Thanks. Yes, this was all done in Manim!

[@harriehausenman8623]

It's 'positive' manim 😉

[@andriyyurachkivsky9756]

7:05 Better to say more accurately 'pairwise disjoint'.

[@ianosborne3101]

These are good videos but they always seem like the end way too early. My advice is to wrap everything up by applying what you have said to what you have shown in the intro. I have no idea what a sigma algebra has to do with the volume of a cube

[@harriehausenman8623]

I really don't mind the 'open-end' but I can see how the videos would benefit from it. 👍