New posts in measure-theory

Haar measure on O(n) or U(n)

Exchange integral and conditional expectation

Monotone class theorem vs Dynkin $\pi-\lambda$ theorem

Lebesgue Integral Over Step Function

Why we impose finite countability to be closed in $\sigma$-algebra $\mathscr{F}$

What exactly is the "Carathéodory Extension theorem"?

When is $F(x)=x^a\sin(x^{-b})$ with $F(0)=0$ of bounded variation on $[0,1]$?

Show that every upper semi-continuous real function is measurable [duplicate]

Difference of elements from measurable set contains open interval

Integration by parts for general measure?

Prove the Countable additivity of Lebesgue Integral.

Derivatives of a series of monotone functions

The space of Riemann integrable functions with $L^2$ inner product is not complete

Continuity almost everywhere

Let $f:A \to \Bbb R^n$ be measurable. Show that $\{x \in \Bbb R^n \mid m(f^{-1}\{x\}) > 0\}$ is a countable set.

Infinitely differentiable functions with compact support are dense in $L^p$

$f$ measurable with $f=g$ a.e. then $g$ measurable

Characterization of a joining over a common subsystem.

representing $E$ as the disjoint union of a finite number of measurable sets that have a measure of at most $\epsilon > 0$

Union of two $\sigma$-algebras is not $\sigma$-algebra