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

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This is part 7 of 22 videos.

#MeasureTheory
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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)

  1. The Bright Side of Mathematics
  2. Mathematics (Field Of Study)
  3. Metric Space
  4. metrischer Raum
  5. Mathematik
  6. Normed Space
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Комментарии
Автор

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!

Mzemze-ox
Автор

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

alphachief