If a sequence of increasing, absolutly continuous functions converges pointwise to a function f, does it follow that f is absolutly continuous? What if it converges uniformly?
2026-02-23 08:28:36.1771835316
Pointwise convergent, increasing sequence
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At least for the pointwise convergence it is definitely wrong. For $f_{n}(x)=x^{n}$, $x\in[0,1]$, these are absolutely continuous, but the pointwise limit is not even continuous.