Measure Theory - Motivation

Real Analysis: We motivate the idea of measure by considering an example where Riemann integration fails. We save measures for the next video, but consider the definition of measure zero.

[thebilla]

Bro you're huge. And good explanation.

[matthewbrenneman]

Great lesson: very clear, easy to understand, relates back to topics that students understand, and every small detail is covered and correct. I wished I had had you as my measure Theory teacher when I was in grad school :)

[ddiq]

Very well done vid and 9 years old at that, if you ever even see this, thanks

[elementbender]

Incredible video- I watched this because I wasn't sure if I wanted to take the Analysis 3 course at my university, but you have me hyped for measure theory; thank you so much!

[marshallross]

Cool video. I like your direct and clear delivery. Thx for posting.

[darthsteeler]

Hey, Bob! This is Ojas, we met and spoke at the JMM in Atlanta! Your videos are great!

[MathDoctorBob]

I need to figure out the long term plan first. Right now I want to get another class up. If I had unlimited resources, a real analysis playlist would be next.

[jongtaekim]

Hi! This video introduces the needs of measurable sets very clearly. I hope to see the next videos!

[MathDoctorBob]

Thanks for the kind words! Still a long way to go, but getting there.

[MathDoctorBob]

It is a convenient description that emphasizes only the topology used.

A simple example is the indiscrete topology on R. The only open sets are the empty set and R itself. So the Borel sets are the empty set and R itself. Any open interval is not Borel (for this topology).

For something more complicated, consider the usual Borel sets on R. A standard exercise is to construct a non-measurable set for Lebesgue measure.

[Zeekless]

Fantastically clear and cool.
Really great thanks for this!

[themilkspots]

Awesome video! Really clear and easy to understand explanation!

[MathDoctorBob]

Still a glimmer in my eye. I'm hoping to have the resources to do real analysis videos once this semester ends.

[benwoodruff]

Fair enough. I am not a "math guy" but measure theory is something I need to understand better as probability only gets me so far in my research.

[maydavidr]

Still hoping for more Dr Bob! mathmonk is well presented but superficial.

[enkii]

Me too, but I have to use measure theory for my research too. Otherwise I ll be kicked out of my program. Hope you make the videos for measure theory fast enough. Thanks again, Bob.

[sukwonlee]

It's really awesome!! I want to watch the next video about measure theory but can't find it. Does anyone know?

[MathDoctorBob]

Not yet. I should get accounts for there, arXiv, and MathOverflow, but I can't imagine the ensuing time sink.

[enkii]

Thanks Bob. Hope he's as good as you.

[enkii]

where is the next video for measurable set?