New posts in Lebesgue Integral

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

How to find $\lim_{n \to \infty}\int_{0}^{1}\sin^2\left(\frac{1}{ny^2}\right)\,\mathrm{d}y$ if it exists?

Swapping integral and sum using dominated convergence theorem

Defining an Antiderivative for Monotone 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.

Evaluating a Lebesgue Integral

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

Multivariable function Integrable for what values?

If $\int_0^1f^k(x)\;dx\le M$, then $m(\{x\in[0,1]:f(x)>1\})=0$.