$\quad A\subset\mathbb{R}$ is measurable and $m(A)>0$. then $m\left(\mathbb{R}-\bigcup_{q\in\mathbb{Q}}q\cdot A\right)=0$.
134310
Minkowski sum of a positive Lebesgue measure set and $\mathbb{Q}$.
29849
How can I show that $\sup(AB)\geq\sup A\sup B$ for $A,B\subset\mathbb{R}$ where $A\cup B$ is positive and bounded?
53425
Prove that there exists a Borel measurable function $h: \mathbb R \to \mathbb R$ such that $g= h\circ f$.
10702
Show that $\left\{A\subset\Omega: A~\text{ is countable or }A^C\text{ is countable}\right\}$ is a $\sigma$-algebra
54791
Is it true or false that $\lvert P([0, 1]) \setminus P((0, 1)) \rvert > \lvert P(\mathbb{N}) \rvert$
154621
A set with a finite integral of measure zero?
86230
$f_n \rightarrow f$ in measure and $g$ be measurable and finite a.e. Prove that $f_ng \rightarrow fg$ in measure
126821
Let $f:[0,1]\to \mathbb{R}$. Show that $\{a \in [0,1]: f(a)\neq 0\} = \bigcup_{n=1}^{\infty} \{a \in [0,1]: |f(a)|\geq 1/n\}$
98717
Are all measure zero sets measurable?
83825
$f^{-1}([-\infty,r))$ measurable for all rational numbers $r$
27615
Prove Borel Measurable Set A with the following property has measure 0.
127720
Prove that $\bigcup_{n \in \Bbb{N}} [1/n,1] = (0,1]$.
82236
Extension of the Lebesgue measurable sets
151707
Fatou's lemma and measurable sets
55461
How to prove that if $a$ belongs to $\mathbb R$, such that $0\leq a \leq\epsilon$, then $a = 0$
98200
$E$ Lebesgue measurable implies $E^2$ Lebesgue measurable?
131664
Why is any Lebesgue-Stieltjes measure on $(\mathbb{R},\mathcal{B}_\mathbb{R})$ not complete?