There exists a sequence of Riemann integrable functions on [0, 1] whose pointwise limit is not Riemann integrable
140618
An example of a sequence of Riemann integrable functions $(f_n)$ that converges pointwise to a function $f$ that is not Riemann integrable.
143240
Convergence of Riemann sums for improper integrals
41057
Does $L^p$-convergence imply pointwise convergence for $C_0^\infty$ functions?
129087
Proof that a sequence of continuous functions $(f_n)$ cannot converge pointwise to $1_\mathbb{Q}$ on $[0,1]$
74339
Integrable function whose Fourier transform is not integrable
156295
Relax Egoroff's Theorem to pointwise convergence a.e. and bounded a.e. pointwise limit
70646
Componentwise Convergence for sequences in $\mathbb{R^{n}}$
151796
There is not an holomorphic function on a bounded domain such that $\lim_{z \to w} f(z)= \infty$ for every $w \in Fr(\Omega)$
127757
$L^1$ convergence gives a pointwise convergent subsequence
151919
Cauchy-Product of non-absolutely convergent series
113790
$\overline{B_1(0)}$ is not weakly* sequentially compact in $(l^\infty)$'
121979
Pointwise convergence of sine series of $x^{-2}$
132713
The space $c_0$ of sequences that converge to 0 is not reflexive
45432
Showing that $f:(0,2\pi]\to S^1$ is not a homeomorphism
154578
Proving there is a sequence convergent to a limit point of a set without axiom of countable choice?
151936
Pointwise Convergence and Convergence in the mean of Riemann-integrable functions
12913
space of riemann integrable functions not complete