There is a measurable set $E \subset [0,1]$ such that $0 < \frac{m(E \cap (a,b))}{b-a} < 1$
38581
Construct a Borel set on R such that it intersect every open interval with non-zero non-"full" measure
134310
Minkowski sum of a positive Lebesgue measure set and $\mathbb{Q}$.
80350
$\limsup \frac{a_n}{b_n}0$ s.t $a_n\le Mb_n$
136795
A non-measurable set of given outer measure
121367
Let $\alpha \in (0,1)$. Find a Borel subset $E$ of $[-1,1]$ s.t. $\lim_{r\to 0^{+}} \frac{m(E\cap [-r,r])}{2r}=\alpha.$
21068
Is composition of measurable functions measurable?
7681
How can this theorem about weakly measurable functions on $\sigma$-finite measure spaces be deduced from the finite measure space case?
98580
Lebesgue-measurable sets requiring the Axiom of Choice to construct
77482
Continuous and preserves measurability $\implies$ preserves null sets.
113778
Show that $E=\{(x,\alpha)\mid 0\leq \alpha<|f(x)|\}$ is measurable if $f$ is measurable.
134770
For sets $A,B$, $A \cap (B \setminus A) \subseteq \varnothing$
146707
Formally show that the set of continuous functions is not measurable
137257
The Supremum and Infimum of a sequence of measurable functions is measurable
144817
Proving Caratheodory measurability if and only if the measure of a set summed with the measure of its complement is the measure of the whole space.
22558
Vitali-type set with given outer measure
97557
supremum of uncountable families of Borel measurable functions
151707
Fatou's lemma and measurable sets