- E2
[19Q] Note:Similar to point [8] from exercise [1J3].Suppose \(f_ n:[a,b]ββ\) are Riemann-integrable, and \(f:[a,b]ββ\) a generic function.
Find an example where \(f_ nβ_ n f\) pointwise, \(f\) is bounded, but \(f\) is not Riemann integrable.
Show that, if the convergence is uniform, then \(f\) is Riemann integrable and
\[ \lim _{nββ} β«_ a^ b f_ n\, {\mathbb {d}}x= β«_ a^ b f\, {\mathbb {d}}x\quad . \]Solution 1
EDB β 19Q
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Authors:
"Mennucci , Andrea C. G."
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