Proving that the counting measure is a measure on $\mathcal A$
18429
Counting measure proof
98897
Proving that the set of $\nu$ measurable sets $M\subseteq P(X)$ is an algebra
14048
Proof that the complement of zero-measure set on $[0,1]$ is dense in $[0,1]$
46056
If $\mathcal{E}$ are subsets of $X$ and $A \subset X$. Show that $\mathcal{A}\mathcal{(E \cap}$ A)=$\mathcal{A}\mathcal{(E)} \cap$ A
42794
Prove that functions map countable sets to countable sets
94438
Show that the countable product of metric spaces is metrizable
52301
Omitting the hypotheses of finiteness of the measure in Egorov theorem
119549
Prove the even integers are countable (by explicitly giving a bijection $\mathbb{N} \to E$)
6161
The cartesian product $\mathbb{N} \times \mathbb{N}$ is countable
55157
$\sigma$-algebras on a countable set is generated by partitions of the set
99562
"Sum" of positive measure set contains an open interval?
102113
Proof that the number of proofs is countably infinite
51260
Sum of sets of measure zero
92309
The $\sigma$-algebra of subsets of $X$ generated by a set $\mathcal{A}$ is the smallest sigma algebra including $\mathcal{A}$
58347
$L^p$ spaces and counting measure
73869
$\mathcal{C}_1 \subseteq \mathcal{C}_2 \implies \sigma( \mathcal{C}_1) \subseteq \sigma( \mathcal{C}_2) $
18223
Prove that the union of two disjoint countable sets is countable