New posts in Measure Theory

Dominated convergence theorem and Cauchy's integral formula

Definition of Lebesgue measurable functions- Why Borel sets?

Prove that the integral $\int_a^b \frac{\sin(x)}{x}dx$ is bounded uniformly.

For $W=\cup_{U\in\mathcal U} U$ show that there exists $U_1,\dots,U_n: \ \sum_{i=1}^n \lambda(U_i) > \frac{1 - \epsilon}{3^d}\lambda(W)$

Intuitive, possibly graphical explanation of why rationals have zero Lebesgue measure

Why does the number of possible probability distributions have the cardinality of the continuum?

$(\int f_1d\mu)^2+\cdots+(\int f_nd\mu)^2\leq(\int \sqrt{f_1^2+\cdots+f_n^2}d\mu)^2$

'Amount' of nowhere-differentiable functions in $C([0,1])$?

Existence of a measurable function such that the pushforward of a measure is equal to another measure

Prove that there is no probability measure on $\mathbb{N}$