Existence of a subset $S\subset\mathbb R$ s.t. $\forall a<b$, $S\cap [a,b]$ has Lebesgue measure $(b-a)/2$?
37361
Is there a measurable set $A$ such that $m(A \cap B) = \frac12 m(B)$ for every open set $B$?
99562
"Sum" of positive measure set contains an open interval?
49143
Showing $A \subset B \iff A\cap B=A$
84263
A Lebesgue measure question
140668
Union of $2$ set $A, B$ where $ A$ is a subset of $B$
86309
Whether the set $A$ is a compact subset of $M_3(\Bbb R)$.
42358
Find a Borel subset satisfying the condition
147237
If $A$ and $B$ are compact subsets of $\mathbb R$, then so is $\frac{A}B$.
151707
Fatou's lemma and measurable sets
134310
Minkowski sum of a positive Lebesgue measure set and $\mathbb{Q}$.
105358
In a second countable space any base has a countable subset that is still a base
69857
Is the set $A=\{x\in E|\lim_{n \to\infty} f_n(x)\ exists\ (finitely)\}$ measurable?
28391
Prove the compactness of a set B
73927
Is $\mathbb{R}$ a subset of $\mathbb{R}^2$?
135112
Outer measure of product of sets
93419
Let $\mathcal A$ be a collection of pairwise disjoint subsets of a $\sigma$-finite measure space,Show that $\mathcal A$ is at most countable.
107160
Open Set and Measure Theory