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Questions about abstract measure and Lebesgue integral theory. Also concerns such properties as measurability of maps and sets.

4 votes
Accepted

strick inequality for Fatou theorem

This is just the definition of convergence for sequences of functions : $\forall x \in \mathbb R, \lim_{n \to+\infty} f_n(x) =0$, which is of course the case here, all sequences $(f_n(x))$ being stati …
Henri's user avatar
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4 votes

Zariski closed sets in C^n are of measure 0

Clearly, it is sufficient to show it for a closed set given by $f=0$ where $f$ is analytic (write your set as included in a countable union of such described sets). Then, using the normal form of anal …
Henri's user avatar
  • 2,727