$A$ a proper subset of $[0,1]$ and $m(A \cap [a,b])\leq \frac{b-a}{2}$ for every interval $[a,b]$
27615
Prove Borel Measurable Set A with the following property has measure 0.
95294
Dense subset of $C[0,1]$ which preserves rationals
82628
Cardinality of a set of closed intervals
73869
$\mathcal{C}_1 \subseteq \mathcal{C}_2 \implies \sigma( \mathcal{C}_1) \subseteq \sigma( \mathcal{C}_2) $
257
Prove that : $m_{a}m_{b}m_{c}\leq\frac{Rs^{2}}{2}$
17461
Show that a set is dense in $[-1,1]$
122326
Proving $|P(A\cap B)-P(A)P(B)|\leq \frac{1}4$
96133
Prove that $ m_{a} \geq m_{g} \geq m_{h} $ using strict inequalities unless $ a = b $.
115606
Proofs involving $ (A\setminus B) \cup (A \cap B)$
131983
Prove that $A \subset B$ if and only if $A \setminus B = \emptyset$
13167
Prove $A = (A \setminus B) \cup (A \cap B)$
106756
Union and Intersection of Sets $A_{i}$ and $B_{j}$
123753
In a metric $(X,d)$, prove that for each subset $A$, $x\in\bar{A}$ if and only if $d(x,A)=0.$
155999
How to prove the following properties of infimum and supremum involving the union and intersection of the sets $A_k$
157218
If $E\subseteq X$ is connected, $E\cap A\neq\emptyset$ and $E\cap(X\setminus A)\neq\emptyset$ then $E\cap\partial A\neq\emptyset$
106927
How do I prove $[G:H\cap K]\leq [G:H][G:K]$?
19289
complement of a set and its measure