Measure theory: show that $f^{-1}(\sigma(\mathcal A)\subset \sigma(f^{-1}(\mathcal A))$
87203
Preimage of generated $\sigma$-algebra
65334
Show that a certain set is measurable
157599
what is the meaning of $F_\sigma$ and $G_\delta?$
127522
Space $\mathcal{L}^p(X, \Sigma, \mu)$ is separable iff $(\Sigma, \rho_\Delta)$ is separable
88418
Proof of a theorem saying that we can make a measurable function continuous by altering it by a set of arbitarily small measure
81112
Proving that the dual of the $\mathcal{l}_p$ norm is the $\mathcal{l}_q$ norm.
98897
Proving that the set of $\nu$ measurable sets $M\subseteq P(X)$ is an algebra
120273
Showing that a collection of sets is a $\sigma$-algebra: either set or complement is countable
94469
How to prove that $|HK| = \dfrac{|H| \; |K|}{|H \cap K|}$?
29637
$\sigma$-algebra of sets that are both $G_\delta$ and $F_\sigma$
3296
Proof That $\mathbb{R} \setminus \mathbb{Q}$ Is Not an $F_{\sigma}$ Set
26369
Proving seemingly obvious equations with measure theory
38946
Show that $\{\cup_{n\in K} (n, n+1]: K \subset \mathbb{Z}\}$ is a $\sigma$-algebra on $\mathbb{R}$
88278
Show $S = f^{-1}(f(S))$ for all subsets $S$ iff $f$ is injective
86230
$f_n \rightarrow f$ in measure and $g$ be measurable and finite a.e. Prove that $f_ng \rightarrow fg$ in measure
120442
Prove Borel sigma-algebra translation invariant
27615
Prove Borel Measurable Set A with the following property has measure 0.