New posts in measure-theory

Is there a dense subset of [0,1] of measure 1/2 whose complement is also dense?

measure-theory examples-counterexamples

Example of strictly subadditive lebesgue outer measure

measure-theory elementary-set-theory

Random variables defined on the same probability space with different distributions

probability measure-theory probability-distributions

Finding simple, step, and continuous functions to satisfy Lebesgue integral conditions

real-analysis measure-theory

Is integration by substitution a special case of Radon–Nikodym theorem?

integration measure-theory

Finitely additive measure over $\mathbb{N}$, under AD.

measure-theory set-theory descriptive-set-theory

Is there a nonmeasurable set in R in which all the measurable subsets are countable?

$C_c(X)$ dense in $L_1(X)$

functional-analysis measure-theory

Every subset of $\mathbb{R}$ with finite measure is the disjoint union of a finite number of measurable sets

Monotone increasing sequence of random variable that converge in probability implies convergence almost surely

measure-theory probability-theory convergence-divergence

Sum of two closed sets is measurable

Open set whose boundary is not a null set

general-topology measure-theory

Uniform $L^p$ bound on finite measure implies uniform integrability

real-analysis integration measure-theory uniform-integrability

The difference between convergence in $L^{\infty}$ and almost uniformly

real-analysis measure-theory

Why do we call it a $\sigma$-algebra?

measure-theory soft-question

every subset of a measurable set is measurable

How to find a function that minimize the following expectation

probability-theory measure-theory

$\mu \otimes \nu(A \times B)=\mu(A)\nu(B)$

probability probability-theory measure-theory set-theory

Is there an open dense set $S \subset [0,1]$ such that $m(S)<1$?

Fubini and induction for a sum over a set $Q$

integration measure-theory induction fubini-tonelli-theorems