Proof about σ-algebra
35140
Existence of minimal $\sigma$-algebra and transfinite induction
146006
Uncountable $\sigma$-algebra
137446
Show that if $b_k\uparrow \infty$ and $\Sigma_{k = 1}^\infty a_kb_k$ converges, then $b_m \Sigma_{k = m}^\infty a_k → 0$ as $m → \infty$.
146795
Proof If $AB-I$ Invertible then $BA-I$ invertible.
81040
proof about commutative operators and T-cyclic vectors
105333
Generated $\sigma$-algebras with cylinder set doesn't contain the space of continuous functions
110832
$F_\sigma$-subsets in a normal space can be separated
117133
Is there an infinite countable $\sigma$-algebra on an uncountable set
73869
$\mathcal{C}_1 \subseteq \mathcal{C}_2 \implies \sigma( \mathcal{C}_1) \subseteq \sigma( \mathcal{C}_2) $
38946
Show that $\{\cup_{n\in K} (n, n+1]: K \subset \mathbb{Z}\}$ is a $\sigma$-algebra on $\mathbb{R}$
7681
How can this theorem about weakly measurable functions on $\sigma$-finite measure spaces be deduced from the finite measure space case?
94980
Measurable functions in a countable co-countable $\sigma$-algebra
83665
Prove a assertion concerning Lebesgue space
18839
Proof about inner product space $\vert \langle x,y\rangle \vert=\Vert x \Vert\Vert y \Vert$
29637
$\sigma$-algebra of sets that are both $G_\delta$ and $F_\sigma$
55157
$\sigma$-algebras on a countable set is generated by partitions of the set
52966
Rings, ideals and units-proof