Measure Theory 7 | Monotone Convergence Theorem (and more) [dark version]

[@saniyakhan2004-h4u]

This is very beautiful the way you explaind. Here is a request, please mention at least one example on each theorem or lemma. It'll be helpful in applications. Thank you!

[@brightsideofmaths]

Great suggestion!

[@alphachief65]

I'm not following an aspect of the part b proof. As far as I can tell, what was proven is: Suppose A is a subset of X. Then if f(A) = g(A), g(X-A) = 0, and f(X-A) >= 0, then the lebesgue integral of f over X is greater than or equal to the lebesgue integral of g over X. As we have not actually addressed something like, for instance, g(x) = f(x)/2. A function where everywhere f(x) > 0, g(x) > 0

[@user-en8wj6vb7z]

very nice lecture!

[@brightsideofmaths]

Many thanks! :)