Measure Theory 13 | Lebesgue-Stieltjes Measures

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This is part 13 of 22 videos.

#MeasureTheory
#Analysis
#Integral
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I hope that this helps students, pupils and others. Have fun!

(This explanation fits to lectures for students in their first and second year of study: Mathematics for physicists, Mathematics for the natural science, Mathematics for engineers and so on)

[peterlee]

I haven't commented on any of your previous videos, but I just want to say how thankful I am that you have made these fantastic lectures available to the public!

[Anteater]

I’m 2 weeks behind in lectures as with online covid lectures, the lecturer goes so fast as he doesn’t have to write! These videos are brilliant. Thanks.

[ChainWasp]

I am truly amazed by measure theory. I'm currently studying stochastic calculus and I am reviewing my measure theory. In this video, the density you presented at the end, is very interesting. It shows up in the calculation of Expectation for a Random Variable, and the F is basically how you measure that r.v. It's crazy how interconnected everything is. Thank you

[SimpMaker]

Thank you. This is helping paint a pretty picture and intuition.

[happyhedgehog]

Really great videos. I am finding them really helpful. Thank you.

[asmaanaciri]

Thank you for these great videos. They're so helpful

[zeinabharakeh]

Your videos are very useful and very organized!

[shaliniyadav]

Thank you so much Sir
It's very helpful

[seanki]

wow, what an underrated video. Amazing. Thank you!

[fatemekashkouie]

I used to hate measure theory. You made me love it ☺️👍 Thanks

[AlvaroBelmar]

Amazing series all around!! Thanks so much for the great work

[qiaohuizhou]

10:20 Q/ “ It doesn’t matter where the equality sign is, the measure can’t see the jump” ( because the measure is defined by either the difference of left limit or the difference of right limit )
10:40 the interesting measure of interval is when the jump is inside the interval
11:10 Dirac measure
11:24 general case

[kolokolo]

love your vids. Greetings from germany !

[Anteater]

So LS measures means defining the length of an interval by the difference in function values at its endpoints?

[MrWater]

So in the first definition the F is continous from the left and in the second case is continous from the right? May I misunderstood something? Because I've tought that the F to be a distribution function must be continous from the right.

[DylanD-vg]

These videos are great, thanks so much for making these!

[muluegebreslasie]

I really appreciate your video, it's amazing! Regarding (c) what is the largest sigma algebra in R where \mu_[F] is defined, and how can I check \mu_[F] for absolute continuity? Thanks.

Hello Julian!
Using this definition for the LS-measure of an interval (i.e., F(b-) - F(a-)) = mu([a, b)), how could we calculate the measure of a set of the type S = {a}?

[amitozazad]

Guys a quick question, the semiring \mathcal{A} includes the sets like [a, b), but the borel set \mathcal{B(R)} includes the sets like (a, b), [a, b], [a, b) and (a, b] ?

[hanmi]

Hi! I'm still a bit confused about the reason that you chose F(a-), instead of F(a), to calculate the length. Could you explain it a bit further? Thank you!