New posts in Lebesgue Measure

Example of a bounded linear functional $T:L^ \infty \to \mathbb{R}$ which cannot be expressed by an integral $\int_{[a,b]}fg$ for an integrable $f$

Is there a set $A \subset [0,1]$ such that $\int_{A \times A^\text{c}} \frac{\mathrm{d} x \, \mathrm{d} y}{\lvert x - y\vert}=\infty$?

Are there uncountably many disjoint uncountable real null sets?

Why this definition for Lebesgue measurable functions?

$| \int fg|\leq 1$ for any $g\in C_{0}^{\infty}$, $\|g\|_{L^{2}}=1$ then $\|f\|_{L^{2}}\leq1$

Proof of Monotone convergence theorem.

If integral is 0 on any set of measure 1/pi, then the function is 0 a.e.

Prove $A+A=\mathbb{R}$ in which the measure of the complement of $A$ is zero

Lebesgue Measure and Measure

“Most intuitive” average of $P$ for all $x\in A \cap [a,b]$, where $A\subseteq\mathbb{R}$?