Does there exist a measurable subset $E$ such that $\varepsilon < \frac{|E\cap{I}|}{I} < 1-\varepsilon$ for every finite interval I =[a,b]?
27615
Prove Borel Measurable Set A with the following property has measure 0.
135548
Every section of a measurable set is measurable? (in the product sigma-algebra)
128332
Counterexample to "Measurable in each variable separately implies measurable"
125910
Continuity of Integration for a measurable function
82236
Extension of the Lebesgue measurable sets
121367
Let $\alpha \in (0,1)$. Find a Borel subset $E$ of $[-1,1]$ s.t. $\lim_{r\to 0^{+}} \frac{m(E\cap [-r,r])}{2r}=\alpha.$
98717
Are all measure zero sets measurable?
69499
Let $A\subset\mathbb{R}$ a measurable and bounded set. Show that exists for each $0\alpha$.
121504
Supremum of a product measurable function...
58827
Absolute value of a measurable function is measurable
44270
$E$ measurable set and $m(E\cap I)\le \frac{1}{2}m(I)$ for any open interval, prove $m(E) =0$
1474
How to prove limit of measurable functions is measurable
114947
Bounded variation implies Borel measurable
25306
A countable family of point-wise bounded functions defined on finite measurable set is actually uniformly bounded on a closed subset
98897
Proving that the set of $\nu$ measurable sets $M\subseteq P(X)$ is an algebra
137203
Measurable cardinal existence condition
120599
Points of a Measure Zero Sets Covered by Intervals Infinitely Many Times