$\mu(A \cap I) \le a \mu(I)$ implies $\mu(A) = 0$?
27615
Prove Borel Measurable Set A with the following property has measure 0.
34147
$\|u\|\leq \|u+av\| \Longrightarrow \langle u,v\rangle=0$
106398
If $A$ is invertible show that $\det(A) \neq 0$
13162
Prove $\alpha \in R[[x]]$ is a unit iff $a_0 \in R$ is a unit
13415
How to show if $A \subseteq B$, then $A \cap B = A$?
90540
What is wrong in this proof: That $\mathbb{R}$ has measure zero
44270
$E$ measurable set and $m(E\cap I)\le \frac{1}{2}m(I)$ for any open interval, prove $m(E) =0$
135511
$M_a =\{ f\in C[0,1] |\ f(a)=0 \}$ for $a$ $\in$ $[0,1]$. Is $M_a$ finitely generated in $C[0,1]$?
98098
Show that $\mu_{F}$ is a measure on $(\mathbb{R},\mathcal{S})$.
131793
Zero integral of measurable $f$ on every interval implies $f=0$?
65395
Prove that if $\operatorname{rank}(T) = \operatorname{rank}(T^2)$ then $R(T) \cap N(T) = \{0\}$
76148
Show that $\exists c \in \mathbb{R} : f(c) = 0$
80892
Does $\wp(A \cap B) = \wp(A) \cap \wp(B)$ hold? How to prove it?
33030
Proof that $\inf A = -\sup(-A)$
118353
For set of positive measure $E$, $\alpha \in (0, 1)$, there is interval $I$ such that $m(E \cap I) > \alpha \, m(I)$
55461
How to prove that if $a$ belongs to $\mathbb R$, such that $0\leq a \leq\epsilon$, then $a = 0$
131444
Local maximum implies derivative is $0$