Measure Theory 6 | Lebesgue Integral [dark version]

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This is part 6 of 22 videos.

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(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)

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Комментарии
Автор

you have no idea how happy it feels to finally get it

snay
Автор

Hello. I have two questions:

1) What happens if we try to take the Lebesgue integral of a non-measurable function?

2) The Lebesgue integral of a measurable function is defined as that supremum. Why does it always exist?

Thank you for your work.

Lait_au_Miel
Автор

Great video! Have you made any video on how to compute the Lebesgue integral or how to build it in a different way? It is a very well explained video and clear though

marcbanfi
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I don't quite get why we write the integral "over X"... If I want to integrate over other subsets of X, how do I distinguish it in the notation?

emiliograndinetti