Measure Theory 18 | Cavalieri's principle - An example

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This is part 18 of 22 videos.

#MeasureTheory
#Analysis
#Integral
#Calculus
#Measures
#Mathematics
#Probability

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)

[ruihansun]

Brilliant video! Many thanks :) I am curious if it possible to make a series in stochastic process in the future?

[AbdulrahmanSOmar]

I'm almost done with this series and I've just become a supporter on Steady! Your videos are incredibly informative and lucid! I piggy-back on the other commentator in voting for a stochastic process series in the future :)

[eduardocambiaso]

I'm going to support u on steady as soon as I can, I love your work!

[aymanbaklizi]

Thank you for this wonderful work. As a remark, the transcript at the bottom of the page sometimes hide your writing and it is difficult to follow you in those moments. I wonder if these transcripts can be removed or put somewhere else.
Thank you again.

[eduardocambiaso]

One question, I tried getting the volume of the unit sphere with this, first thinking of the area of a circle in R^2 (pi times r^2), taking the radius to be 1-z when z € [0, 1] (I took the volume of a semi sphere and then planned to multiply that by 2). So I get the M subset (the one in R2) to be {(x, y) € R^2 : x^2 + y^2 <= (1-z)^2} and the measure of these sets is pi · (1-z)^2. integrating this in z€[0, 1] I get that the area of a semi circle is pi/3, and multiplying it by 2 (so it becomes the area of a circle and not a semi circle) i get 2pi/3. What did I do wrong? It should be 4pi/3, but I can't figure out what i am doing wrong

[OnlyOnePlaylist]

I am kind of struggling with understanding the part at 7:00 where you just use an antiderivative to solve the integral. How do we know that the Lebesgue integral w.r.t the Lebesgue measure is equal to the antiderivative (like the Riemann integral does)? We haven't proved this

[darthvasilisn]

I am a little confused in the substitution of μ2(Μz0) (in 5:30). Could you please explain it more thoroughly?

[redaabakhti]

brilliant exposition please do more videos in english and thanks a lot

[masoumehvahedi]

This is wonderful video, many thanks. Could you provide the reference link?

[phymatcosmos]

Can you please make all your videos in English which are in German, I really enjoyed your measure theory course.

[ilyboc]

Finally some calculations lol... it was too abstract :s