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If {f_n}:ℝ→ℝ are measurable and f_n-->f pointwise, then convergence is a.e. uniform. Are there any conditions we can add to have f_n-->f in some open interval (a,b)?

Correction: convergence happens in some subset of finite measure; otherwise above not true.

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# Measurable and Unif. Convergence in (a,b)

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