Prove that sin(x)/x is not Lebesgue Integrable in [1,+oo]
101546
Lebesgue integral $\int_{(0, \infty)} \frac{\sin x}{x} dm$ doesn't exist but improper Riemann integral exists
46642
Continuity of $\sin(x)/x$
38185
Prove that $\{\cos(nx) : n=1, ... ,\infty \}$ is bounded but not totally bounded in $C([0,\pi])$
108955
Showing $(\mathbb{Q},+)$ is not isomorphic to $(\mathbb{R},+)$
35319
I'm looking for several ways to prove that $\int_{0}^{\infty }\sin(x)x^mdx=\cos(\frac{\pi m}{2})\Gamma (m+1)$
94244
$\sin \frac{1}{x}$ is not uniformly continuous on $[1, \infty]$
63453
A proof of the fact that the Fourier transform is not surjective from $\mathcal{L}^1(\mathbb{R})$ to $C_0( \mathbb{R})$
61267
List of functions not integrable in elementary terms
86537
Prove that an open interval and a closed interval are not homeomorphic
75888
How to prove the function $y = \sin x$ is not a closed function?
83966
Does $ \int_0^{\infty}\frac{\sin x}{x}dx $ have an improper Riemann integral or a Lebesgue integral?
41659
Limit as $x\to 0$ of $x\sin(1/x)$
35569
Prove that $[0,1]$ isn't homeomorphic to $\mathbb{R}$
55839
Interior of the Graph of $\sin(1/x)$
108816
$L^p$ integrable but not $L^q$ integrable
99485
Prove that $1/f$ is Riemann integrable on $[a,b]$
25996
Using the definition of Riemann integrability, prove that $f $is Riemann integrable on $[0,1]$