(PP 1.1) Measure theory: Why measure theory - The Banach-Tarski Paradox

A playlist of the Probability Primer series is available here:
http://www.youtube.com/view_play_list?p=17567A1A3F5DB5E4

You can skip the measure theory (Section 1) if you're not interested in the rigorous underpinnings. If you choose to do this, you should start with "(PP 1.S) Measure theory: Summary" at:
http://www.youtube.com/watch?v=upISxgopsFU&p=17567A1A3F5DB5E4

(0:00) Intro to Probability Primer series.
(1:20) Why do we need measure theory? We illustrate the need using the remarkable Banach-Tarski Paradox.

Category:

Education

Tags:

• measure theory
• probability
• math

[chogo888]

thank you for these videos. You must be a wonderful person to put up great tutorials such as these for free and put so much effort into them

I am looking forward to watching other videos in your series

thanks

[mathematicalmonk]

@chogo888 Thank you for your kind words! Just knowing that people are benefiting from the videos, through comments like yours, makes it truly worthwhile. Besides, I get a kick out of math, and sharing that experience with others is pure joy.

[Javadhajipoor]

Thank you so much, actually I was looking for such a video and I am so lucky that this video has just been uploaded yesterday. But the problem is that the videos have not numbers, so it is difficult to find the video right after the first one.

[mathematicalmonk]

@Javadhajipoor You are very welcome! I'm so glad it was helpful to you. Thank you for the wonderful suggestion about numbering (which you will see I have adopted). Do let me know if you have any further suggestions.

[ricardovencio]

This is like Khan's Academy on steroids ;-) thanks!

[MrImpliedvol]

great video. thanks so much for this

[MegaMayorca]

alfred tarski and bunach were amazing

[PHDBurmount]

Great videos. However I should comment that remark 1 on the definition of a sigma-algebra, requires the property of finite aditivity to be proven first.

[Ma7m9d]

Interesting!..A choice can be made to reject the axiom of choice.

[MyOverflow]

@THE16THPHANTOM #2. That's why it is called a paradox.

[69erthx1138]

Just found your videos surfing for stuff on stochastic calculus. Nice take on Banach-Tarski.

[THE16THPHANTOM]

what is meant by those two balls?

#1 that the two balls added together make up the same volume as the first. which makes sense.

#2 that each of those balls are the same volume as the first one. which does not make sense. there for the measure theory says yes each one is the same volume

[Schwyndfst]

¡Gracias Monje Matematico! This helps me reading Big Rudin!

[wshp90]

You speak so slowwwwww

[labpib]

Very good material. I told my grad students to watch them and then we will discuss the lectures at classroom. As Khan from Khan academy says "I assign the lectures for homework, and what used to be homework, I now have the students doing in the classroom". Thanks from Brazil.