New posts in Measure Theory

What's the intuition behind the Co-Area formula?

Can you draw a curve that captures light?

The converse problem about duality of $L^p$

Cartesian product of two collections of sets?

Showing two measures are equal up to scalar multiplication.

On the proof of The Bounded Convergence Theorem

Prove that $x \mapsto \boldsymbol{\mathrm P} \left[ \mathrm{B}(\boldsymbol\cdot + x ) \in A \right]$ is measurable for a Brownian motion $\mathrm B$

Extremal distribution of random variable that averages to a given value

Prove that for independent random variables $X_i$, we have $f_i(X_i)$ are independent.

What does the limit of the characteristic function $\varphi(x)\xrightarrow{\lvert x\rvert\rightarrow \infty} 0$ tell us about $\mu(\{a\})$?