More measurable set, measure zero and measurable function

More measurable set, measure zero and measurable function

0:00 start
7:00 definition of Borel set
9:00 not all borel set is measurable
12:00 measure zero
18:20 definition of a measurable function
23:30 if f is a measurable function, then the absolute value of f is a measurable function
25:00 if fn is a measurable function, then limit sup is a measurable function
27:51 the composition function of two measurable sets is measurable

Advanced mathematics list:

Real analysis:
https://www.youtube.com/playlist?list=PLg9w7tItBlZsaSW0zlQ7m0S3Ti51bYJg_

Group representation for finite group
https://www.youtube.com/playlist?list=PLg9w7tItBlZvxk4eus_gi2Wp3yYAEXF9-

exact sequences
https://www.youtube.com/playlist?list=PLg9w7tItBlZuI7n7notRRA2jol69e9mc9

Ring theory lecture
https://www.youtube.com/playlist?list=PLg9w7tItBlZtfPKHWGlU55kqafEgUu45u

group theory lecture
https://www.youtube.com/playlist?list=PLg9w7tItBlZtSHrTTVjEzAsUcO69YXY7v

Category theory
https://www.youtube.com/playlist?app=desktop&list=PLg9w7tItBlZtI1njDjtXt_0Hkqbn9RVvi

Field theory in abstract algebra
https://www.youtube.com/playlist?list=PLg9w7tItBlZtA6XhMIgIPkgj_SDKChbN-

Mathematical analysis
https://www.youtube.com/playlist?list=PLg9w7tItBlZu-yFYxQrWrFKcdOHRz2Fkh

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