New posts in measure-theory

For every null set $E$ there is a measurable set $F$ with different upper and lower Lebesgue density at every point of $E$

real-analysis measure-theory

Measurability of almost everywhere continuous functions

measure-theory lebesgue-measure

Constructing a Measure on the Rational Numbers

real-analysis measure-theory

Is the space of probability measures on a compact set is compact w.r.t Wasserstein metric?

functional-analysis probability-theory measure-theory metric-spaces

number of sigma algebras on finite sets?

Is $\delta$ in $L^\infty$?

measure-theory lebesgue-measure distribution-theory dirac-delta

Associativity of product measures

Probabilistic Proof of $\prod\limits_{i=1}^\infty\cos\left(\frac t{2^i}\right)=\frac{\sin t}t$ [duplicate]

real-analysis probability probability-theory measure-theory trigonometry

Prove convergence in $L^1$ if norms in $L^2$ are uniformly bounded

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

intuition of decomposition of $\mathbb{R}$ into disjoint union of first category and null set

real-analysis measure-theory real-numbers baire-category

Probability of selecting a non-measurable set

Definition of the product $\sigma$-algebra

real-analysis measure-theory

$\int_X f^p d\mu = p\int_{[0,+\infty)} t^{p-1}\mu(\{x\in X: f(x)>t\}) d\mu_t$ for any natural $p\ge 1$ [duplicate]

real-analysis measure-theory lebesgue-integral

An uncountable family of measurable sets with positive measure

real-analysis measure-theory

A nonnegative random variable has zero expectation if and only if it is zero almost surely

probability-theory measure-theory

Extension of measure is less or equal to outer measure when restricted to semiring [closed]

measure-theory outer-measure

Riemann integral of characteristic function of Cantor set

Lebesgue points of density and similar notions

real-analysis analysis measure-theory lebesgue-measure

What does Fatou's Lemma really say?

Example of an uncountable dense set with measure zero

real-analysis measure-theory examples-counterexamples