New posts in measure-theory

Any linear subspace has measure zero

Does "All additive functions are linear" imply every set of reals is measurable?

Space of probability measures "complete"? (In the other sense)

A Lebesgue measure question [duplicate]

Why is Lebesgue integration better suited for convergence axioms?

Nonmeasurable set with positive outer measure

Understanding the assumptions in the Reverse Fatou's Lemma

Does $\sigma(\cup_{n=0}^\infty \mathcal{F}_{S \wedge n}) = \mathcal{F}_S$ hold for every stopping time $S$?

Let $E$ be measurable and define $f:E\rightarrow\mathbb{R}$ such that $\{x\in E : f(x)>c\}$ is measurable for all $c\in\mathbb{Q}$, is $f$ measurable?

A Fundamental Theorem of Calculus

Examples of non-measurable sets in $\mathbb{R}$

Proving that if $(X_t)_{t\geq0}$ and $(Y_t)_{t \geq0}$ are continuous and have the same marginal distributions, then $P_\mathbb{X}=P_\mathbb{Y}$.

Fast convergence in $L^1$ implies convergence almost everywhere

Explicit description of small open set containing the rationals

Rigorous proof that $\int_{\Omega}X\;dP=\int_{-\infty}^{\infty}xf(x)\;dx$

Proof of the identity $\int_0^{+\infty}\frac{\sin(x)}{x^\alpha}dx=\frac{\Gamma(\alpha/2)\Gamma(1-\alpha/2)}{2\Gamma(\alpha)}$ for $\alpha\in (0,2)$.

A simple curve of positive area

Applications of the 5/8 Theorem

Probability of $\limsup$ of a sequence of sets (Borel-Cantelli lemma)

Is there a solution manual for Royden fourth edition?