How can I find a function $f$ such that $f \notin L^{p} (\mathbb{R})$ for all $p$ but you can find a constant $c>0$ for it with
$m(x \in \mathbb{R} \, s.t. |f(x)|>t) \leq \frac{c}{t}$ for $\forall t$
I tried $f(x)={1 \over x^2}$ since $f \notin L^{p} (\mathbb{R})$ for all $p$, but it looks like this is not the right answer. I guess we could use the Chevyshev's inequality on $f(x)$ , the measure theoretic one (see Section Measure-theoretic statement in https://en.wikipedia.org/wiki/Chebyshev%27s_inequality)