$f:\mathbb{R} \rightarrow[0,\infty) $ is a measurable function, if $\int_{-\infty}^{\infty} f(x)=1$, then $\int_{-\infty}^0\frac{1}{1+f(x)}=\infty$
13287
Let $\int_{- \infty}^{\infty} f(x) dx =1$. Then show that $ \int_{- \infty}^{\infty} \frac{1}{1+ f(x)} dx = \infty.$
87216
Lebesgue non-measurable function
158122
If $f$ is measurable, then support of $f$ is measurable?
6620
If $\lim\limits_{x\rightarrow\infty} (f'(x)+f(x)) =L<\infty$, does $\lim\limits_{x\rightarrow\infty} f(x) $ exist?
25652
Intuitive explanation for $\mathbb{E}X= \int_0^\infty 1-F(x) \, dx$
15001
Multiple choice question: Let $f$ be an entire function such that $\lim_{|z|\rightarrow\infty}|f(z)|$ = $\infty$.
110458
Show that if $f$ is continuous on $(0,1)$ and $\lim_{x \to 0}f(x) = + \infty$ then $f$ is not uniformly continuous
59581
A function which is continuous in one variable and measurable in other is jointly measurable
80643
Show that f(x) defined on [0,infinity) R to is continuous at 0.
137257
The Supremum and Infimum of a sequence of measurable functions is measurable
61133
Show that $\int|f(x)|dx=\int_0^\infty m(E_\alpha)d\alpha$
110395
Integrable function $f$ on $\mathbb R$ does not imply that limit $f(x)$ is zero
124916
$f$ such that $\int_1^{\infty}f(x)dx$ converges, but not absolutely?
813
$f$ uniformly continuous and $\int_a^\infty f(x)\,dx$ converges imply $\lim_{x \to \infty} f(x) = 0$
58361
Is there a continuous function such that $\int_0^{\infty} f(x)dx$ converges, yet $\lim_{x\rightarrow \infty}f(x) \ne 0$?
1474
How to prove limit of measurable functions is measurable
32063
if $f'(x)\rightarrow L$ as $ x \rightarrow \infty$, $-\infty \leq L \leq \infty $ then $ f(x)/x \rightarrow L $ as $x \rightarrow \infty$