If $f_{n}\rightharpoonup \bar{f}$ and $f_{n}(x) \rightarrow f(x)$ pointwise a.e., then is $\bar{f} = f$ a.e.?
67900
Pointwise a.e. convergence and weak convergence in Lp
9957
Prove if $f:[a,b] \rightarrow \mathbb{R}$ is integrable, then so is $|f|$ and $\left|\int_{a}^{b}f(x)dx\right| \leq \int_{a}^{b}|f(x)|dx$
91947
Proof of $ f:I_n \rightarrow I_m \Rightarrow n = m$
59063
$f(f(x))=f(x)$ question
96458
Does $X_n \overset{L^2}{\rightarrow} X$ imply $X_n^2 \overset{L^1}{\rightarrow} X^2$?
148410
How do I show $f_n(x)=n^2 x^n(1-x)$ pointwise converges to $0$ on $[0,1]$?
106830
are $f(f(x))=f(x)$ and $f(x)=x$ equivalent?
77074
If $ f(f(f(x)))=x$, does$ f(x)=x$ necessarily follow?
99526
Is $\lim\limits_{n\rightarrow\infty} n$ comparable to $\aleph_0$?
59187
Proof, is $\forall x : (P(x) \lor Q(x)) \Leftrightarrow \forall x : P(x) \lor \forall x : Q(x)$?
30685
Is $f(a)\!=\!0\!=\!f(b)\Rightarrow (x\!-\!a)(x\!-\!b)\mid f(x)\,$ true if $\,a=b?\ $ [Double Factor Theorem]
153063
Uniform convergence of $f_n(x)=nx^n(1-x)$ for $x \in [0,1]$?
17314
Use property to show that if $f_n \rightarrow f$ in measure on finite measure set $E$ then $f_n^2 \rightarrow f^2$ in measure on $E$.
114702
$\int_0^{\infty} f(x)dx$ converges and $\lim_{x\rightarrow \infty} f(x)$ exists, then $\lim_{x\rightarrow \infty} f(x)=0$?
129551
Does $\lim_{h\rightarrow 0}\ [f(x+h)-f(x-h)]=0$ imply that $f$ is continuous?
57581
Let $E$ be measurable and define $f:E\rightarrow\mathbb{R}$ such that $\{x\in E : f(x)>c\}$ is measurable for all $c\in\mathbb{Q}$, is $f$ measurable?
113450
Construction of a function which is not the pointwise limit of a sequence of continuous functions