Prove that if $A$ is a Borel set, then so is $x + A$, for every $x \in \mathbb{R}$
120442
Prove Borel sigma-algebra translation invariant
56818
Prove that if $A$ is positive, then $\exists\;\alpha>0$ such that $\langle Ax, x \rangle\geq \alpha|x|^2$ for $x\in\Bbb{R}^n$
48523
Let $A$ be any uncountable set, and let $B$ be a countable subset of $A$. Prove that the cardinality of $A = A - B $
68781
proving if $a \le b$ then $\sup(A) \le \inf(B)$
136789
How to prove $a \lt b$ for all $a \in A, b \in B$ implies $\sup A \leq \inf B$?
98897
Proving that the set of $\nu$ measurable sets $M\subseteq P(X)$ is an algebra
69499
Let $A\subset\mathbb{R}$ a measurable and bounded set. Show that exists for each $0\alpha$.
80009
Prove that $| |a|-|b| | \le |a-b|$
18334
Equivalence between CH and existence of certain sets in $\mathbb{R}^2$
145397
How to prove that for every $i$, $a_i = i$
40232
What do we mean when we say "Let $x$ be an element of the set $\mathbb{R}$"?
27615
Prove Borel Measurable Set A with the following property has measure 0.
47856
$f(x)=ax+b$ for some $a,b\in\mathbb{Q}$ if $f(\mathbb{Q})\subset\mathbb{Q}$ and $f(\mathbb{R-Q})\subseteq \mathbb{R}-\mathbb{Q}$
55461
How to prove that if $a$ belongs to $\mathbb R$, such that $0\leq a \leq\epsilon$, then $a = 0$
138202
Every open set in $\mathbb{R}$ is a countable union of closed sets
61810
An application of Borel-Caratheodory theorem
123613
Double Complement of a set proof