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Real-valued functions of real variable, analytic properties of functions and sequences, limits, continuity, smoothness of these.

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A net of lower semicontinuous functions

Assume we have a non-decreasing net of lower semicontinuous functions $f_\alpha:[0,1]\to\mathbb{R}$ such that $\lim_\alpha f_\alpha\to f$ pointwise. Please is it true that one can extract a countable …
Oleg Zubelewicz's user avatar