Show convergence of measurable functions is not induced by convergence of topology
75078
Characterization of Almost-Everywhere convergence
146707
Formally show that the set of continuous functions is not measurable
135656
Why non-measurable sets exist?
125910
Continuity of Integration for a measurable function
129087
Proof that a sequence of continuous functions $(f_n)$ cannot converge pointwise to $1_\mathbb{Q}$ on $[0,1]$
128332
Counterexample to "Measurable in each variable separately implies measurable"
52301
Omitting the hypotheses of finiteness of the measure in Egorov theorem
139612
Follow-up regarding right-continuous $f:\mathbb{R} \to\mathbb{R}$ is Borel measurable
7681
How can this theorem about weakly measurable functions on $\sigma$-finite measure spaces be deduced from the finite measure space case?
1474
How to prove limit of measurable functions is measurable
132713
The space $c_0$ of sequences that converge to 0 is not reflexive
71870
Example of Converge in measure, but not converge point-wise a.e.?
11558
How to show that the limit of compact operators in the operator norm topology is compact
41208
weak convergence in $L^p$ plus convergence of norm implies strong convergence
1332
Pointwise convergence and convergence of integrals implies $L^1$ convergence
59581
A function which is continuous in one variable and measurable in other is jointly measurable
114947
Bounded variation implies Borel measurable