Measure Theory 10 | Lebesgue's Dominated Convergence Theorem [dark version]

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This is my video series about Measure Theory. I hope that it will help everyone who wants to learn about it. We discuss sigma algebra, measures, and integration. For any questions, please leave a comment or come to the community forum of the Bright Side of Mathematics: tbsom.de/s/com...
#MeasureTheory
#Analysis
#Integral
#Calculus
#Measures
#Mathematics
#Probability
This is part 10 of 22 videos.
(This explanation fits to lectures for students in their first year of study: Mathematics for physicists, Mathematics for the natural science, Mathematics for engineers and so on)
The Bright Side of Mathematics has whole video courses about different topics and you can find them here tbsom.de/s/start

[@mreverbel]

I am now in the first year of a master's in statistics, and Measure Theory is used all the time to derive a complete theoretical understanding in my mathematical statistics classes. I find this series so amazingly helpful, having come from a non-pure mathematics background.
So an enormous thanks for this! Everything is so well explained and so clear. Not only the notation and thought process, but also the purpose of measure theory as an analytical tool becomes clear throughout your series. Just wonderful!

[@brightsideofmaths]

Nice! I am very glad that it is helpful. For the notations in probability theory, you can check out my other videos: tbsom.de/s/pt

[@mreverbel]

@@brightsideofmaths Thanks! I have indeed already checked the beginning of your probability course.
I was wondering if you were planning to, in the future, make videos tackling decision theory, and the definition of sufficient statistics, development of hypothesis testing and point estimation? There's a nice bridge to be made between that and Measure Theory.

[@Andrew_J123]

Wanted to comment and say that I'm using this to teach myself measure theory! Thanks for making these!

[@brightsideofmaths]

You're very welcome! Please also use the additional material in the description :)

[@0x90meansnop8]

Danke für's Uploaden der dunklen Version!!! Uns Nachtlerner freut es sehr, besonders unsere Augen!!!

[@lyudvigfeyerbax8659]

In 2024, at the moment, I'm learning Measure theory from this videos, these are very helрful

[@brightsideofmaths]

Nice :) I was hoping that the videos stay relevant longer when creating them.

[@jidebranco2168]

We need a video on Conformal mapping