New posts in Lebesgue Integral

$\lim_{r\to\infty} \int_0^\infty rx/(exp(x) + r^2x)dx = 0$

The relation between uniform integrability and dominated convergence theorem in the case of counting measure

Does the derivative of a differentiable function have to be Lebesgue integrable in some interval?

Dominated convergence theorem and Cauchy's integral formula

Is $f(x)=\sum_{n=1}^{\infty}\frac{x}{1+n^2x^2}$, $x\in[0,1]$ continuous on $[0,1]$

Showing $\lim_{n\to\infty}\int_{\mathbb{R}} f(x)f(x+n) dx=0$

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

Condition for $L^r(\mu)=L^\infty(\mu)$ where $\mu(X)=1$

Lebesgue Integral - Self Learning

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 $f$