Is there a Lebesgue measurable subset $A \subset R$ such that for every interval $(a,b)$ we have $0 < \lambda(A\cap(a,b))< (b-a)$
38581
Construct a Borel set on R such that it intersect every open interval with non-zero non-"full" measure
131793
Zero integral of measurable $f$ on every interval implies $f=0$?
88418
Proof of a theorem saying that we can make a measurable function continuous by altering it by a set of arbitarily small measure
156176
Lebesgue measurability of nearly identical sets
57206
Lebesgue measure on probability measure
98200
$E$ Lebesgue measurable implies $E^2$ Lebesgue measurable?
88602
Inner regularity of Lebesgue measurable sets
60053
Does the boundary of an open set have measure zero (in $\mathbb{R}^n$)?
82236
Extension of the Lebesgue measurable sets
58827
Absolute value of a measurable function is measurable
88610
The set of convergence of a sequence of measurable functions is measurable
56303
Why this definition for Lebesgue measurable functions?
94971
For every $\epsilon>0$ there exists $\delta>0$ such that $\int_A|f(x)|\mu(dx) < \epsilon$ whenever $\mu(A) < \delta$
60868
Interplay of Hausdorff metric and Lebesgue measure
64320
Prove that if $0<a<Pr(A)$ then there exists $B\subset A$ such that $Pr(B)=a$
116676
Examples of uncountable sets with zero Lebesgue measure
67866
If $f:\mathbb{R}\to\mathbb{R}$ is a left continuous function can the set of discontinuous points of $f$ have positive Lebesgue measure?