Possible Duplicate:
examples of measurable functions on $\mathbb{R}$
I am trying to construct a Lebesgue measurable function $f: \mathbb{R}\rightarrow\mathbb{R}$ which has the property that for any open interval $I$,
$\int_I fdm=\infty$.
I have tried a few approaches to this problem. Most recently, I have tried using the density of the rationals by creating a sequence of translations of $1/x$, one with a singularity at each rational, and taking the sup of that sequence (which we know to be Lebesgue measurable since each of the functions in the sequence is Lebesgue measurable). Unfortunately, it seems that the sup of this sequence is infinity everywhere, which is not helpful.
Any hints would be greatly appreciated. Thanks!
