Prove exist a measurable function
53425
Prove that there exists a Borel measurable function $h: \mathbb R \to \mathbb R$ such that $g= h\circ f$.
118195
How does one prove that $e$ exists?
53627
Proving continuity of $f$
7681
How can this theorem about weakly measurable functions on $\sigma$-finite measure spaces be deduced from the finite measure space case?
151707
Fatou's lemma and measurable sets
110146
I need to prove the continuity of $f(x)=\log x$ using a $\epsilon-\delta$ proof
60032
If the measure of union = sum of outer measures, then the sets are measurable
139151
How to prove $\left\{ \omega|X(\omega)=Y(\omega)\right\} \in\mathcal{F}$ is measurable, if $X$ and $Y$ are measurable?
148247
Prove the existence of an analytic function
47187
Proving the measure of an increasing sequence of measurable sets is the limit of the measures
22597
Composition of measurable function and continuous function
41683
Pre-image of a measurable set A is always measurable?
9159
$L^p$-norm of a non-negative measurable function
128332
Counterexample to "Measurable in each variable separately implies measurable"
87216
Lebesgue non-measurable function
115219
If $E$ is Lebesgue measurable, show that there exists a closed set $F$ with $F \subset E$ and $m(E\setminus F)<\epsilon$
94781
Prove that $M(t)=\sup_ {a \leq x \leq t} f(x)$ given $f(x)$ is continuous on $[a,b]$