Measurable function $f: \mathbb{R} \to (0,\infty)$ with $\int \chi_If d\lambda = \infty$ for every open interval of $\mathbb{R}$
85208
Is there a function with infinite integral on every interval?
94971
For every $\epsilon>0$ there exists $\delta>0$ such that $\int_A|f(x)|\mu(dx) < \epsilon$ whenever $\mu(A) < \delta$
95260
Let $m$ be Lebesgue measure and $a \in R$. Suppose that $f : R \to R$ is integrable, and $\int_a^xf(y) \, dy = 0$ for all $x$. Then $f = 0$ a.e.
47992
Is there a function $f\colon\mathbb{R}\to\mathbb{R}$ such that every non-empty open interval is mapped onto $\mathbb{R}$?
115878
Continuous unbounded but integrable functions
135999
One sided limit of an increasing function defined on an open interval
40564
Prove that $u(x,t)=\int_{-\infty}^{\infty}c(w)e^{-iwx}e^{-kw^2t}dw\rightarrow 0$ if $x\rightarrow \infty$
52632
$f\colon(0,\infty)\to \mathbb R$ be continuous ; $f(x)\le f(nx) , \forall n \in \mathbb N , \forall x >0$ , then $\lim_{x\to \infty} f(x)$ exists?
158423
How to prove that if $f$ is continuous a.e., then it is measurable.
75735
Let $f$ be a continuous function on an interval around $0$ and let $a_i=f(\frac{1}{i})$ (for large enough $i$)
70512
Prove that $\int f\ d\lambda = \int_{a}^{b} f(x)\ dx,$ for any $f \in \mathcal R[a,b].$
125190
Convergence to function that is not measurable
131793
Zero integral of measurable $f$ on every interval implies $f=0$?
95429
If $f$ is continuous with $ \int_0^{\infty}f(t)\,dt<\infty$ then which are correct?
10747
Given function $g$ continuous in line $[0,\infty)$...
22597
Composition of measurable function and continuous function
19452
Restriction of a Lebesgue integral to a subset of a measurable set.