Show that a $\sigma$-algebra is either finite or uncountable.
43894
If $S$ is an infinite $\sigma$ algebra on $X$ then $S$ is not countable
128437
How to prove that a finite set is countable
121141
Proving Finiteness of Group from Presentation
32965
Proving that for infinite $\kappa$, $|[\kappa]^\lambda|=\kappa^\lambda$
115860
Is a measure for a sigma algebra determined by its values for a generator of the sigma algebra?
19297
Is the cofinite topology on an uncountable set first countable?
63860
Measure of Dependence Between Two $\sigma$-algebras
19996
Example where union of increasing sigma algebras is not a sigma algebra
147783
Showing a sigma algebra is the union of certain collection of sigma algebras
115120
Finite dimensional $C^*$-algebras
116955
Showing the existence of a certain kind of extension of a finitely generated algebra
55157
$\sigma$-algebras on a countable set is generated by partitions of the set
94980
Measurable functions in a countable co-countable $\sigma$-algebra
103307
Generate the smallest $\sigma$-algebra containing a given family of sets
81327
union of sigma algebra is sigma algebra
153306
Number of sigma algebras for set with 4 elements
73869
$\mathcal{C}_1 \subseteq \mathcal{C}_2 \implies \sigma( \mathcal{C}_1) \subseteq \sigma( \mathcal{C}_2) $