No Lebesgue-measurable subset such that $\lambda(I\cap A) = \frac{1}{2} \lambda(I) \forall I$
63413
For a set of positive measure there is an interval in which its density is high, $\mu(E\cap I)> \rho \mu(I)$
128332
Counterexample to "Measurable in each variable separately implies measurable"
41683
Pre-image of a measurable set A is always measurable?
135694
Proving $\kappa^{\lambda} = |\{X: X \subseteq \kappa, |X|=\lambda\}|$
65334
Show that a certain set is measurable
117533
$|A-\lambda I|$ and $|\lambda I-A|$
44430
Is there an open dense set $S \subset [0,1]$ such that $m(S)<1$?
1474
How to prove limit of measurable functions is measurable
84359
On Lebesgue Outer Measure of an interval
131793
Zero integral of measurable $f$ on every interval implies $f=0$?
112323
Showing that $f = 0 $ a.e. if for any measurable set $E$, $\int_E f = 0$
63538
Impossibility of constructing a continuum-size linearly independent set in $\Bbb R$
116676
Examples of uncountable sets with zero Lebesgue measure
155311
How to get a set $E$ such that $0<\mu(E\cap I)<\mu(E)$ for all interval $I$?
87216
Lebesgue non-measurable function
44270
$E$ measurable set and $m(E\cap I)\le \frac{1}{2}m(I)$ for any open interval, prove $m(E) =0$
35713
Let $X\subset \mathbb{R}$ Lebesgue measurable, $|X|<|\mathbb{R}|$, is it true that $X$ is null?