Probability and Measure Lecture 1: What is a Measure?

In this video, we introduce some of the main definitions in Measure theory. This includes measures and sigma-fields and some examples to set the stage for future lectures.

[QuantAgent]

You're a true professor.
Do you know who is called a professor?
it's not the one who can assimilate knowledge, but the one who can transform knowledge from higher dimensional space into lower dimensional space, so uninitiated people can learn!

Thank you professor for sharing your gifted teaching ability with us.

[JTan-fqvy]

Why the measure (which is a function) need to be countable additive? Specifically, the equation given for the countable additive seems obvious; so I am curious if there is any non-trivial measure (function) that makes the equation not hold (i.e., it's not crafted specifically to violate countable additivity)?

[sucramgnat]

God bless your kind soul! No words can express my appreciation for you.

[suxianzhou]

I just opened your video, and your opening is awesome. I can't wait to watch it !!

[parnzaa]

You're so clearly explained! Thank you so much for uploading this.

[arunabhoroy]

Sir, what book do you recommend for studying probabilistic measure theory?

[sallanmega]

Thanks for sharing! Greetings from Spain

[yaarrated]

any good book for introduction to measure theory and probability? I am currently reading through the Measure Theory by D.H.Fremlin but it's kinda hard to wrap my head around...

[FieldDebby-oh]

Smith Dorothy Harris Gary Davis Sandra

[alessandraespejo]

Thank you so much, this was really helpful for me. I wish I had you as a Professor. It would be unimaginable if my professor followed your program.

[YYHo-kwbi]

Thanks you for your sharing! I need advanced probability source snd I am lucky to have your course!

[WangKamden]

thank you so much for transforming such a tedious topic into an interesting one.

[kimyongtan]

Thank you professor for sharing the lecture, it helped me a lot!

[siyunli]

great advanced probability theorem based on measure theory, enjoy watching it . Dear professor, will you upload more statistics course in future?

[MrTrixever]

Love this, thank you so much professor!

[fernandojackson]

Prof Kashlak, excellent lecture. I believe at 40:27, it should be the union of [-i, -i-1]. Your union can be made disjoint if you use half-open intervals, [i, i+1), etc., defining m([a, b})=m[[a, b]]=b-a. Thanks to you, your school for the great lecture, material. I know all this is obvious to you, guess yu just made a small mistake.

[konstantinosbanos]

Hello Professor, can you tell me how your board application is called? Thank you in advance!

[smurasame]

Is it any textbook for reference? Thank you so much!

[helensol]

Finally I got the measure theory. Thank you so much! Can you do the same with the Functional Analysis?

[yannickbrunink]

Finally an explenation I understand!! Thanks