New posts in real-analysis

Could we ever hope to integrate all functions?

real-analysis integration set-theory axioms descriptive-set-theory

Proving that $\lim_{s \to 0^-} \int_{0}^{\infty} \frac{\arcsin(\sin x)}{x} x^{s} \, dx = \int_{0}^{\infty} \frac{\arcsin(\sin x)}{x} \, dx $

real-analysis integration limits fourier-series mellin-transform

A set with a finite integral of measure zero?

real-analysis measure-theory

A version of Hardy's inequality involving reciprocals.

real-analysis calculus sequences-and-series inequality cauchy-schwarz-inequality

Conditions for continuous extension of a function on an open set to its closure

real-analysis analysis continuity

Uniform Convergence: The two definitions

Proof that a linear transformation is continuous

real-analysis proof-verification continuity

About uniformly continuity for bounded and continuous function

real-analysis analysis continuity uniform-continuity

Taylor series (or equivalent at $\epsilon\to0$) of the integral over $x$ of a function of $x$ and $\epsilon$

real-analysis integration power-series taylor-expansion

An infinite $\sigma$-algebra contains an infinite sequence of nonempty, disjoint sets.

real-analysis measure-theory

Scratch work for delta-epsilon proof for $\lim_{x \to 13} \sqrt{x-4} = 3$

real-analysis proof-verification

Prove the derivative of $x^2 \sin (1/x^2)$ is not (Lebesgue) integrable on $[0,1]$

Rigorous proof for the converse of $\lim_{x \to \infty} f(x) \implies f $ is uniformly continuous

real-analysis uniform-continuity

Generalized nested sine function [closed]

real-analysis calculus fractional-iteration

Show that $\sum_{n=3}^{\infty}f_n$ is uniformly convergent in $(-\pi,\pi)$ for $f_n := \ln(\cos(\frac{x}{n}))$

real-analysis calculus sequences-and-series

Proving that $\int_0^1\frac{x \log^2(1-x)}{1+x^2} \ dx = \frac{35}{32}\zeta(3)+\frac{1}{24}\log^3(2) -\frac{5}{96} \pi^2 \log(2)$

calculus real-analysis integration definite-integrals

If $f(x)+\frac{f'(x)}{x}\to0$ then $f(x)\to0$

real-analysis limits

A limit evaluating to $2 K$ (Catalan's constant)

real-analysis calculus limits definite-integrals catalans-constant

Computing $\sum_{n=1}^{\infty} \left(\psi^{(0)}\left(\frac{1+n}{2}\right)-\psi^{(0)}\left(\frac{n}{2}\right)-\frac{1}{n}\right)$

calculus real-analysis sequences-and-series

Proof of fundamental lemma of calculus of variation.

real-analysis calculus-of-variations