Measure Theory 1 | Sigma Algebras [dark version]

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This is part 1 of 22 videos.

00:00 Introduction
00:58 Measuring lengths
03:00 Example power set
03:51 Definition sigma-algebra
10:20 Example for sigma-algebras

#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)

[jms]

Note to future viewers: at 9:58 when he says blue sets he actually means the yellow rectangular sets A_i, because the colours have been inverted!

[JaGWiREE]

Thanks so much. I have a rare disease called corneal neuralgia which involves photophobia, so this dark version aids me a lot and helps relieve a lot of tension that distracts my focus.

[janwyczawski]

Definitely one of my favourite series on this channel. It is insane how well you explain these concepts. I feel like most math channels on youtube either strive for maximum simplicity, which makes the videos very easy to understand but also pretty shallow, or they keep them in a format of a lecture which often goes very in-depth but doesn't feel much more accessible than a book or lecture notes. You however, especially in this series, manage to do both - keep the videos captivating and easy to understand while still conveying all the important ideas, enough to get a good understanding of like 80% of the core concepts and then be able to easily go through any book on the topic to fill in the details.

[durgeshanand]

I knew equation wise what the sigma algebra and the conditions meant but visualizing it with Venn diagrams really helped understand the matter. thanks a lot. sigma algebra feels real now just like numbers on the number line. earlier it made no sense, just existed because some dude said so.

[Heisenberg]

Is there any significant difference of illustration between this dark version and the bright version which I have followed before?

[Ganerrr]

instead of re-uploading all your videos in dark mode u can just make a channel called "the dark side of mathematics" lol

(but seriously dark mode makes videos 100x better on my eyes)

[_Sam_-zhsw]

i know its wrong to be so demanding and i really apologize for it. But is it possible for you to make two playlists which include relavant maths videos for financial engineering and machine learning?

[oldcowbb]

is there a particular reason closed under uncountable union is not necessary?

[lordstevenson]

Black background is much better than the dark blue imo