New posts in measure-theory

Is my understanding of product sigma algebra (or topology) correct?

general-topology measure-theory

Prove that set $A=\{(x,y)\in \mathbb{R}; \left|x\right| + \left|y\right|=q; q \in \mathbb{Q}\}$ has measure $0$

real-analysis measure-theory

Countably generated sigma-algebras

measure-theory set-theory examples-counterexamples descriptive-set-theory

Finitely additive measures on $2^\mathbb{N}$

Show $\lim\limits_{n\to\infty}\int_{0}^{\infty}e^{-x}\sin(\frac{n}{x})~\text{d}x=0$

real-analysis measure-theory

Does $f_n \to 0$ in $L^1(\mathbb R^2)$ imply that $f_{n_k}(x,\cdot)\to 0$ in $L^1(\mathbb R)$ for almost every $x \in \mathbb R$?

measure-theory convergence-divergence lebesgue-integral

Definition of "deterministic coupling" [Villani]

analysis measure-theory optimal-transport

Definition of predictable process

measure-theory stochastic-processes stochastic-calculus

Convergence of Integrals implies almost everywhere convergence of functions

measure-theory probability-distributions lebesgue-integral pointwise-convergence

Prove that in $\mathbb{R}$, if $|a-b|>\alpha$ for all $a\in A$ and $b\in B$, then outer measure $m^(A\cup B)=m^(A)+ m^*(B)$

real-analysis measure-theory

Construct a continuous monotone function $f$ on $\mathbb{R}$ that is not constant on any segment but $f'(x)=0$ a.e.

real-analysis measure-theory

It is possible to define our intuitive notion for probability in subsets of $[0,1]$

measure-theory probability-theory definition intuition

Non-ergodic measure

measure-theory probability-theory dynamical-systems ergodic-theory

Properties of absolutely continuous functions

Lebesgue measure question on carefully-defined subset of $[0,1]$ and showing that it is measurable

How to show that the event that a prisoner does not go free is not measurable

probability-theory measure-theory axiom-of-choice paradoxes

Show that a straight line has a lebesgue measure of zero

"Sum" of positive measure set contains an open interval?

general-topology measure-theory

Show $f$ is in $L^p$ given Markov-like inequality

real-analysis analysis measure-theory lebesgue-measure lp-spaces

Proof of Lusin's Theorem

real-analysis measure-theory