Measure and Integration 16 - Fatou's lemma and Monotone Convergence Theorem

In this lecture, we prove Fatou's lemma and Monotone Convergence Theorem and see some of the consequences of these results.
Follow my website to get full lecture notes: sites.google.com/view/bsreddy...

[@biplabsaikia7853]

thank you sir for this kind of good explanation 👍👍

[@user-pq2jv7nj2t]

thank you for perfect explanation

[@komal_b252]

Thank you sir

[@ajaykumarprajapati6096]

There is some inorder editing still it is a helpful lecture on fatou's lemma

[@wenanyaugustine3311]

Ohh my God you are so good. Am sad though this is the last video you posted on the course, hopefully you can post the next and the next topics.

[@BSReddy.Tech4Trends]

Thank you, there are 24 videos for this course, you can check measure and integration playlist for all vidoes

[@wenanyaugustine3311]

I know . I just wish you could post more videos past the absolute continuity. With no disrespect to my Prof but you are the best, very few would expand on proof the way you do.

[@BSReddy.Tech4Trends]

If time permits, I will prepare few courses in near feature. Where are you from?

[@BabasabTakatrao]

Sir plz I need scope, motivation of Measure and integration for synopsis and dissertation

[@bishalsaha4899]

Sir how integral over a set of measure zero is zero ? Could you explain

[@takeshi_yamato]

Hi Professor! Thanks for this amazing lecture. In the proof of Fatou's lemma, I wonder what failure would arise if we force to use limsup instead liminf. Is it because limsup doesn't exist?

[@BSReddy.Tech4Trends]

Very good observation dear Takeshi Yamato. Definitely we can have Fatou’s lemma interms of limsup. Can you see from the proof that the inequality get reversed if we want to state interms of limsup? Just remember how integral is defined interms of sup and inf. Please let me know if you can’t state and prove interms of limsup, will help you.

[@takeshi_yamato]

sorry professor. i tried but i couldn't see how the usage of limsup would reverse the inequality. i thought we could just apply it to the line """integral of hn over E

[@BSReddy.Tech4Trends]

@@takeshi_yamato in this proof we have considered h

[@takeshi_yamato]

Now I understood it. Thank you so much, Professor! Your lectures are really helpful.

[@BSReddy.Tech4Trends]

@@takeshi_yamato Happy to see that my lectures are useful. Where are you studying ?

[@user-pq2jv7nj2t]

I need solution for measure theory

[@sudampadhan2314]

Yes

[@arunprasath.r2911]

Missing there is no proper editing

[@BSReddy.Tech4Trends]

I am sorry for that. All my lectures are live and not edited. Let me know exactly where you are having problem, so that i can explain you that part.

[@arunprasath.r2911]

There is no full video of monotone convergence theorem only half proof sir

[@arunprasath.r2911]

Sir are you from tamilnadu

[@BSReddy.Tech4Trends]

@@arunprasath.r2911 Yes, you are right, I think some part is not recorded, so sorry for that. If you want I can share pdf of the missing proof.

[@BSReddy.Tech4Trends]

@@arunprasath.r2911 no, I’m from Andhra Pradesh, now settled in Nanded, Maharashtra

[@abhaygupta4461]

Thanks sir