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4:22 exactly what I was looking for... Thank you! Greetings from Portugal 🙂

I didn't know your TH-cam channel, I found this video very enjoyable :), thanks! And by the way, I found also this exercise kind of difficult, one might think that the solution is easier.

Fantastic video.

Thanks so much!

Ethan, I may be wrong but I noticed at 7:12 I don't think you took the p-th root of the second term, ie the one that becomes the measure. Or am I wrong?

Very helpful. Thx

It's amazing that I found one of my former classmates in this vídeo. Congratulations Andrés! You made it!

Great video, thanks :)

I really wish there were more of these videos. Great work.

math4ai3 check

Thank you Dr . Can I chat with you

Very good explanation 👍😊 thank you sir...

So helpful... Thanks

The Smith Chart used in RF/Microwave Engineering is an example of a Möbius Transformation. arxiv.org/pdf/1201.4068.pdf

From iraq to you Thanks for that

Q1)For positive real numbers, square root is ALWAYS a positive quantity. So, root of 4 is +2 and never -2. The confusion comes from x^2=4 ==> x=+/-2 and the incorrect/lazy way some instructors do it by writing x^2=4 ==> x= oot{4} ==> x= +/-2 which should instead be x=+/- oot{4}. Q2) OMG! Why isn't everyone shouting out the simple refutation that "what is $x$ many times if $x$ is not an integer?!" Because something is written down on a page does not mean it is valid in to begin with. Since we intend to take d/dx we must consider x being non-integer.

Thank you Ethan!!

Thank you for the vidéo just continue and go ahead

Love this! I think the input should be -1/3 instead of 1/3? Either way, it doesn't change the bound since we take the modulus. Edit: Actually, I realized that I was using a different fractional transform, (i-z)/(i+z), which is a negative version of the Cayley transform.

Edit: In the statement of Holder's inequality, I do need that f, g are measurable even though that is (kind of) implied by the conclusion.

Great work! I'm learning real analysis myself and it's nice to see well presented problems on it in video form. Subscribed for more and have good luck studying for prelims :)